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

Given : ∠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

∠PSQ =   (3 x + 18)  ,  ∠QSR  = 9x - 27

To Find : measure of ∠PSQ in degrees

Solution:

∠PSR = ∠PSQ + ∠QSR

∠PSR = 99°

∠PSQ = 3x + 18

∠QSR  = 9x - 27

99  = 3x + 18 + 9x - 27

=> 99 = 12x - 9

=> 108 = 12x

=> x = 9

∠PSQ = 3x + 18

= 3* 9 + 18  

= 45

∠PSQ = 45°

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