Question

In this question I cannot figure out what will be the value of x. Kindly, let me know.

Answer 1

IF RT = UT,

then by theorem, if two opposite sides are equal then, their corresponding opposite angles will also be equal.

Then in triangle RTU,

Angle T + Angle R + Angle U = 180 °
Let angle R and U be a.

2a + 114 = 180

2a = 180 - 114

2a = 66

a = 33 °

By exterior angle property,

The sum of two interior angles is equal to the exterior angle in a triangle.

Angle S + Angle U = Angle x

31 + 33 = x

x = 64 °

So, OPTION C is correct.