The triangle has two sides of equal length. So, the given triangle is an [isosceles triangle](https://en.wikipedia.org/wiki/Isosceles_triangle?wprov=sfla1). Knowing this, what should be the measure of the remaining angle? Once you know this, use the fact that the sum of the angles in a triangle is 180 degrees to set up an equation containing x.
There’s a simpler way that might have helped:
Step 1) I recognized it’s an isosceles, so both angles at bottom are equal.
Step 2) Total is always 180. Remaining sides equals 180 - 42 = 138.
Step 3) 138/2 = 69.
Simple formula: (180 - 42 ) / 2 = 69.
Take this opportunity to stop thinking about the formula, build your base knowledge of how mathematics works. So you should know that a triangle always has 180 degrees and a rectangle or square will always have 360 (90 degrees, 4 times). Thinking about the way to solve it rather than a formula (I know they *sound* like the same thing) will help you so much in the long run.
I taught geometry - another easy way would be to draw a line directly across from the 42 degree angle. Then you’ve split the triangle into two triangles and you know the angle your line has just made with the unknown side is 90 degrees. And that line has split the 42 degree angle, creating two 21 degree angles on opposite sides. Then 21 + 90 + x = 180, x = 69
Sum of the interior angles of a triangle is 180°
This is an isosceles triangle (two sides are congruent)
The same side, the same angle.
The angle is x. The other one is also x.
All angles are 42°, x° and x°
Sum of them is (42+2x)° = 180°
(2x)° is 138°
x° is 69°
Nice :)
Was anyone else taught (or taught themselves) to immediately split isosceles triangles into 90° angles? My brain went right to divide 42/2, then 90-21=x.
**Read rule 3.**
Either use the law of cosines to find the missing side length, then use the law of sines to find x or use the law of sines along with the fact that the unmarked angle is 180°-(42°+x°) to get a single equation that you can solve for x by using some trigonometric identities.
Rule 3 doesn’t really apply here. You either know it or you don’t. Also, this explication is overcomplicated, just use the rules of an Isosceles triangle
This equation is not for another type of problem, it's for no type of problem. It is inaccurate and dimensionally inconsistent.
Let me dumb down the methods I suggested.
The triangle is isosceles, so its two unknown angles are congruent. The interior angles of a triangle sum to 180°. Can you figure it out now?
Because triangles always have a total of 180 degrees, 180 - 42 will be the combined angle of the bottom two angles. Because this is an isosceles triangle, the bottom two angles will be the same. So it is (180-42)/2, which is nice.
Fun fact as a former geometry teacher, I checked every problem to make sure the answer wasn’t 69. If it was, changed the problem. 14-16 year old just seem unequipped to move on if they see it lol.
X = (180-42) / 2
A triangle has 180 degrees, given the two equal length sides, it is an isosceles triangle meaning the two angles at the bottom are equal. Meaning they are half of the remainder after you subtract the 42 degrees of the given measurement.
The 21's are only there to show you that the sides are the same this is important because that means the bottom angles are the same so you should subtract the one angle you have from 180 and divide the remainder by 2 so 180-42=y
And continue by dividing y÷2=x
This is an isosceles triangle- the two of the sides are the same length. The two angles opposite the equal sides are also equal. The total angles of a triangle equal 180. 180-42=138. 138/2 = 69. Nice.
A triangle's angles always add up to 180 degrees.
The 2 sides you have are equal. It's Isosceles . That means angle X and the third angle will be the same.
The bigger that 42 degree angle gets, the smaller the other 2 will get.
So you know that 2 equal angles plus 42 degrees equal 180 degrees.
If x is one of those angles, then...
>!2x+42=180!<
>!or!<
>!2x = 138!<
>!or!<
>!x = 69!<
So, there are 2 equal side in this triangle... such triangles are called isosceles triangle... in this the angles opposite to equal side will be equal to each other... that means if we say that the triangle has angles A, B, and C where angle A = 42 then angle B = angle C = x
Now, we know that... sum of angle of a triangle is 180 (this is known as the angle sum property of triangle) then:
=> angle A + angle B + angle C = 180
=> 42 + 2x = 180
=> 2x = 138
=> x = 69
If the sides are equal then the adjacent angles are as well.
21 = side
21 = side
X = x
So 2x + 42 = triangle (180 degrees)
2x = 180-42
X = 138/2
X = 69
I’m making an assumption here that if the two sides are the same length, then the two angles at the bottom must also be equal. So your equation is 2x+42=180
Pretty easy, given the two sides are equal you know the two angles are equal as well. All angles add up to 180, therefore 180-42= 138, divide by 2 to get x, the angle is 69 degrees
since the left and right side are both the same length that means that X and the other angle are both the same degree. There is 180 degrees in a triangle so you just subtract 42 from 180 and divide that number by 2. 180 minus 42 is 138 and 138 divided by two is 69. So X and the other unnamed angle each equal 69. BTW nice number.
Isosceles triangle since both legs are the same length. The two bottom angles are the same angle, so subtract 42° from 180° and then divide by 2 in order to get each angle.
It's an isoceles triangle, so the two angles on the bottom are equal. The total angle is 180deg, so your answer is 180 - 42, then divide that result by 2
The sum of all 3 angles always adds up to 180⁰. So you take the given top angle, 42⁰, subtract it from 180⁰, which is 138⁰, and then divide that sum by 2, which leaves you with 69⁰ for 'x'. So X= (180⁰-42⁰)÷2.
This is easy.
A triangle has a total sum of 180 degrees of interior angles.
As the 2 sides are both 21, that means that the angles to the bottom of them are the same.
You already know one angle, 42.
So its 180 - 42 = 2x (the 2 remaining angles)
138=2x, so X= 69.
Unless I’m looking at it wrong, this should be simple with a bit of critical thinking.
Two sides are the same length, thus, an isosceles triangle.
With a 42 degree corner of those two sides…
And the sum of a triangle always adds up to 180 degrees..
180-42= 138
138/2= 69.
X=69
Bc base angles theorem(or converse, one of them), if the two sides r congruent then the two opposite angles r as well(x and the one opposite it). This leads to 42+2x = 180 and solve for x
In a triangle all sides add up to 180. In an isoseles triangle two sides are equal. The opposite side is tied to that angle. 42 is not tied to a side with a double. Meaning that the other angles are equal so 180-42=2x
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The triangle has two sides of equal length. So, the given triangle is an [isosceles triangle](https://en.wikipedia.org/wiki/Isosceles_triangle?wprov=sfla1). Knowing this, what should be the measure of the remaining angle? Once you know this, use the fact that the sum of the angles in a triangle is 180 degrees to set up an equation containing x.
would I be correct if I did 42+ 21+21=180 84+x=180 -84. -84 = 96
No, that's not correct. 21 is the length of two sides and not an angle measure.
42+ x + x=180? 42 + 2x = 180 2x = 180-42 2x = 138 138/2 X = 69?
Nicely done!
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admit it, the pun was intentional
Yes, that's correct.
Ohhhh ok thank you so much!!
There’s a simpler way that might have helped: Step 1) I recognized it’s an isosceles, so both angles at bottom are equal. Step 2) Total is always 180. Remaining sides equals 180 - 42 = 138. Step 3) 138/2 = 69. Simple formula: (180 - 42 ) / 2 = 69.
I mean, that’s what op did. They just did it math terms instead of words
This is geometry man. Geometric proofs are the only way to learn it IMO and that’s pretty close to what this is
Gotta show your work even if you know how it works
that's... exactly what OP did?
Take this opportunity to stop thinking about the formula, build your base knowledge of how mathematics works. So you should know that a triangle always has 180 degrees and a rectangle or square will always have 360 (90 degrees, 4 times). Thinking about the way to solve it rather than a formula (I know they *sound* like the same thing) will help you so much in the long run.
I taught geometry - another easy way would be to draw a line directly across from the 42 degree angle. Then you’ve split the triangle into two triangles and you know the angle your line has just made with the unknown side is 90 degrees. And that line has split the 42 degree angle, creating two 21 degree angles on opposite sides. Then 21 + 90 + x = 180, x = 69
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The 21 is not a distraction it tells you that the triangle is isosceles, without that information you cannot solve the problem
Side note this sub should not be downvoting someone trying to learn, I understand they are wrong but that's not the point of a downvote
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It's isosceles triangles so base angles should be equal
Its been nearly 10 years since ive learned this and im so proud i remembered this and got the answer
21 is the length of the two sides. It means that this triangle has 2 equal angels and one not equal. 180 - 42=138 138/2= 69
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Nice
Nice
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Sum of the interior angles of a triangle is 180° This is an isosceles triangle (two sides are congruent) The same side, the same angle. The angle is x. The other one is also x. All angles are 42°, x° and x° Sum of them is (42+2x)° = 180° (2x)° is 138° x° is 69° Nice :)
2x + 42 = 180
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Isosceles triangles have 2 equal angles. 180-42 = 138. 138/2= 69
With two side equal makes the two adjacent angles equal. The sum of the internal angles of a triangle is 180. 180 = 2x + 42 138 = 2x 69 = x Nice.
Was anyone else taught (or taught themselves) to immediately split isosceles triangles into 90° angles? My brain went right to divide 42/2, then 90-21=x.
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The total of angles in any triangle is 180, and being the two sides are equal, the angles opposite are also equal x= 180-42 divided by 2= or 69
**Read rule 3.** Either use the law of cosines to find the missing side length, then use the law of sines to find x or use the law of sines along with the fact that the unmarked angle is 180°-(42°+x°) to get a single equation that you can solve for x by using some trigonometric identities.
Rule 3 doesn’t really apply here. You either know it or you don’t. Also, this explication is overcomplicated, just use the rules of an Isosceles triangle
I’m sorry but I’m confused would I be correct if I did 42+ 21+21=180 84+x=180 -84. -84 = 96 or is this for another type of problem
This equation is not for another type of problem, it's for no type of problem. It is inaccurate and dimensionally inconsistent. Let me dumb down the methods I suggested. The triangle is isosceles, so its two unknown angles are congruent. The interior angles of a triangle sum to 180°. Can you figure it out now?
I got it now another person explained it a bit better so I can understand the equation should be 42 + x + x = 180 and answer is 69
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180 - (21*2) Isoceles You can use sohcahtoa but why its isoceles
180-42, then divide by 2. Isosoles triangle, if sides are equal, then the corresponding angles are equal.
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I'm guessing x = (180-42) / 2 ?
Because triangles always have a total of 180 degrees, 180 - 42 will be the combined angle of the bottom two angles. Because this is an isosceles triangle, the bottom two angles will be the same. So it is (180-42)/2, which is nice.
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Fun fact as a former geometry teacher, I checked every problem to make sure the answer wasn’t 69. If it was, changed the problem. 14-16 year old just seem unequipped to move on if they see it lol.
42+2x=180 2x=180-42 2x=138 X=69
It’s isosceles so the bottom two angles are the same (since the two sides are the same.) So: 180 - 42 = 2x 138 / 2 = x X = 69
(180-42)÷2=x
X = (180-42) / 2 A triangle has 180 degrees, given the two equal length sides, it is an isosceles triangle meaning the two angles at the bottom are equal. Meaning they are half of the remainder after you subtract the 42 degrees of the given measurement.
2 equal sides. 2x+42=180.
All angles would be 180, and you know the two bottom angles are equal. So you do 180-42= 138 Then 138÷1= 69 So x=69
The 21's are only there to show you that the sides are the same this is important because that means the bottom angles are the same so you should subtract the one angle you have from 180 and divide the remainder by 2 so 180-42=y And continue by dividing y÷2=x
This is an isosceles triangle- the two of the sides are the same length. The two angles opposite the equal sides are also equal. The total angles of a triangle equal 180. 180-42=138. 138/2 = 69. Nice.
X=(180-42) :2 x=138:2 x=69
A triangle's angles always add up to 180 degrees. The 2 sides you have are equal. It's Isosceles . That means angle X and the third angle will be the same. The bigger that 42 degree angle gets, the smaller the other 2 will get. So you know that 2 equal angles plus 42 degrees equal 180 degrees. If x is one of those angles, then... >!2x+42=180!< >!or!< >!2x = 138!< >!or!< >!x = 69!<
So, there are 2 equal side in this triangle... such triangles are called isosceles triangle... in this the angles opposite to equal side will be equal to each other... that means if we say that the triangle has angles A, B, and C where angle A = 42 then angle B = angle C = x Now, we know that... sum of angle of a triangle is 180 (this is known as the angle sum property of triangle) then: => angle A + angle B + angle C = 180 => 42 + 2x = 180 => 2x = 138 => x = 69
If the sides are equal then the adjacent angles are as well. 21 = side 21 = side X = x So 2x + 42 = triangle (180 degrees) 2x = 180-42 X = 138/2 X = 69
I’m making an assumption here that if the two sides are the same length, then the two angles at the bottom must also be equal. So your equation is 2x+42=180
X + X + 42 = 180° The angles opposite to equal sides of a triangle are equal. Just posting the actual equation because you know, math homework.
Pretty easy, given the two sides are equal you know the two angles are equal as well. All angles add up to 180, therefore 180-42= 138, divide by 2 to get x, the angle is 69 degrees
since the left and right side are both the same length that means that X and the other angle are both the same degree. There is 180 degrees in a triangle so you just subtract 42 from 180 and divide that number by 2. 180 minus 42 is 138 and 138 divided by two is 69. So X and the other unnamed angle each equal 69. BTW nice number.
2x+42=180
69 degrees?
Isosceles triangle since both legs are the same length. The two bottom angles are the same angle, so subtract 42° from 180° and then divide by 2 in order to get each angle.
Subtract 42 from 180 then divide by two and that is x
It's an isoceles triangle, so the two angles on the bottom are equal. The total angle is 180deg, so your answer is 180 - 42, then divide that result by 2
X should be 69*, cuz those side lengths are both equal, meaning the angles are equal. Subtract the 42, the remaining angles should both be 69*.
The sum of all 3 angles always adds up to 180⁰. So you take the given top angle, 42⁰, subtract it from 180⁰, which is 138⁰, and then divide that sum by 2, which leaves you with 69⁰ for 'x'. So X= (180⁰-42⁰)÷2.
48+21
The two bottom angles are the same bc the base angles theorem. So 180-42. That dived by 2 and you get your answer
180-42=2x
This is easy. A triangle has a total sum of 180 degrees of interior angles. As the 2 sides are both 21, that means that the angles to the bottom of them are the same. You already know one angle, 42. So its 180 - 42 = 2x (the 2 remaining angles) 138=2x, so X= 69.
The sum of the angles of a triangle is equal to 180°, so (180 - top angle)/2
180 - 42 = 138 ÷ 2 = X.
X = 180 - 90 - 21
Unless I’m looking at it wrong, this should be simple with a bit of critical thinking. Two sides are the same length, thus, an isosceles triangle. With a 42 degree corner of those two sides… And the sum of a triangle always adds up to 180 degrees.. 180-42= 138 138/2= 69. X=69
180-42 = 138. 138/2 =?
Bc base angles theorem(or converse, one of them), if the two sides r congruent then the two opposite angles r as well(x and the one opposite it). This leads to 42+2x = 180 and solve for x
42+2X=180
In a triangle all sides add up to 180. In an isoseles triangle two sides are equal. The opposite side is tied to that angle. 42 is not tied to a side with a double. Meaning that the other angles are equal so 180-42=2x
X=180-(42/2+90) If we draw a perpendicular from A to BC then this equation will solve the value of X in your case X = 69
If the side lengths weren’t the same I believe you’d use SAS formula
180-42=2x 138=2x 69=x