In the figure, RT = TU. What is the value of x?

Explanation

Choice C is correct. To solve for x, first recognize that ∆RTU is an isosceles triangle since RT = TU. The base angles ∠TRU and ∠TUR are therefore congruent. Using the triangle sum theorem, we find that 114° + 2t° = 180°, solving for t gives 33°. ∠TUR is congruent to ∠SUV, so ∠SUV also measures 33°. According to the triangle exterior angle theorem, the measure of an exterior angle (x°) is equal to the sum of the measures of the two non-adjacent interior angles. Therefore, x = 31° (∠VSU) + 33° (∠SUV) = 64°.Choices A, B, and D are incorrect because they either miscalculate the angle measures or fail to apply the exterior angle theorem correctly.