Question

Angle PSR measures 99°.

Point S has three lines extending from it. One line extends to point P, another to point Q, and the other to point R. Angle P S Q is (3 x + 18) degrees. Angle Q S R is (9 x minus 27) degrees.
What is the measure of AnglePSQ in degrees?

9°
24°
45°
54°

Answer 1

Angle PSR is the sum of angles PSQ and QSR, so
99 = (3x + 18) + (9x − 27) = 12x − 9
12x = 108 → x = 9.
Then PSQ = 3x + 18 = 27 + 18 = 45°.

Answer: 45°.