Question

in the figure above, rt = tu. what is the value of x?
a) 72
b) 66
c) 64
d) 58

Explanation:

Step1: Find ∠RTU's base angles

Since \( RT = TU \), \( \triangle RTU \) is isosceles. Let \( \angle TRU=\angle TUU = y \). The sum of angles in a triangle is \( 180^\circ \), so \( 114^\circ + 2y=180^\circ \). Solving for \( y \): \( 2y = 180 - 114 = 66 \), so \( y = 33^\circ \).

Step2: Use exterior angle theorem

In \( \triangle RSV \), \( \angle SVU \) is an exterior angle. The exterior angle theorem states that an exterior angle of a triangle is equal to the sum of the two non - adjacent interior angles. So \( x^\circ=\angle S+\angle TRU \). We know \( \angle S = 31^\circ \) and \( \angle TRU = 33^\circ \), so \( x=31 + 33=64 \).

Answer:

C) 64