Question

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

Explanation:

Step1: Find ∠STV

$\angle STV = 180^\circ - 114^\circ = 66^\circ$

Step2: Find ∠SUV

$\angle SUV = 180^\circ - 31^\circ - 66^\circ = 83^\circ$

Step3: Identify isosceles triangle angles

Since $RT=TU$, $\angle TRU = \angle SUV = 83^\circ$

Step4: Calculate ∠RVT

$\angle RVT = 114^\circ$ (vertical angle to $\angle STU$)

Step5: Solve for $x$

$x = 180^\circ - 83^\circ - 33^\circ = 64^\circ$

Answer:

C) 64