Question

What is m∠PTQ?

Line segment PS and QR crosses each other at the point T. The angle PTQ is (x + 28) degree. The angle RTS is (2x + 16) degree.

A. 12°
B. 40°
C. 50°
D. 140°

Answer 1

Explanation:

Angle PTQ and Angle RTS are vertical angles.

Vertical angles are congruent:

( x + 28 ) = ( 2x + 16 )

Solve for x:

x + 28 - 16 = 2x + 16 - 16

x + 12 = 2x

x + 12 - x = 2x - x

12 = x

Put 12 in place of x for PTQ and Solve:

PTQ = ( x + 28 )

12 + 28 = 40

Angle PTQ = 40 degrees, so the answer is B.