Problem 1
Answer: x = 60
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Work Shown:
For any triangle, the three angles always add to 180.
60+60+x = 180
x+120 = 180
x = 180-120
x = 60
This triangle is considered equiangular because all angles are equal. It is also equilateral meaning all sides are the same length.
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Problem 2
Answer: x = 134
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Work Shown:
We'll use the remote interior angle theorem. This is where we add two interior angles, and that sum is equal to an exterior angle that is not adjacent to any of the interior angles mentioned.
So basically we can say
x = 64+70
x = 134
If you want a longer method, then let y be the missing interior angle of the triangle. Note how 64+70+y = 180 which solves to y = 46. Then note how y+z = 180 since the angles y,z are a linear pair. That means y+z = 180 turns into 46+z = 180 which solves to z = 134.
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Problem 3
Answer: x = 36
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Work Shown:
Use the remote interior angle theorem
(interior angle1)+(interior angle2) = remote exterior angle
(24) + (2x+18) = 3x+6
2x+42 = 3x+6
42-6 = 3x-2x
36 = x
x = 36
