Question

In Triangle A B C, what is the value of x?

Triangle A B C. Angle A is 112 degrees. Exterior angle to angle B is 2 x degrees and the exterior angle to angle C is (2 x + 12) degrees.

Answer 1

x = 70.

Reason: Let the interior angles at B and C be B and C. If the exterior at B is 2x then B = 180 − 2x, and if the exterior at C is 2x+12 then C = 180 − (2x+12) = 168 − 2x. Sum of angles: 112 + (180 − 2x) + (168 − 2x) = 180 → 460 − 4x = 180 → x = 70.