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

Options

A. 72
B. 66
C. 64
D. 58

Answer

C

Explanation

Since RT = TU, it follows that `triangleRTU` is an isosceles triangle with base RU. Therefore, `angleTRU` and `angleTUR` are the base angles of an isosceles triangle and are congruent. Let the measures of both `angleTRU` and `angleTUR` be `t^@`. According to the triangle sum theorem, the sum of the measures of the three angles of a triangle is `180^@`. Therefore, `114^@ + 2t^@ = 180^@`, so t = 33.
Note that `angleTUR` is the same angle as `angleSUV`. Thus, the measure of `angleSUV` is `33^@`. According to the triangle exterior angle theorem, an external angle of a triangle is equal to the sum of the opposite interior angles. Therefore, `x^@` is equal to the sum of the measures of `angleVSU` and `angleSUV`, that is, `31^@ + 33^@ = 64^@`. Thus, the value of x is 64.
Choice B is incorrect. This is the measure of `angleSTR`, but `angleSTR` is not congruent to `angleSVR`. Choices A and D are incorrect and may result from a calculation error.