What is the measure of PSQ in degrees? Angle PSR measures 99°.

Solution:

Given, angle PSR = 99°

From the figure,

Angle PSQ = (3x + 18)°

Angle QSR = (9x - 27)°

We have to find the value of angle PSQ.

We know, ∠PSR = ∠PSQ + ∠QSR

99° = (3x + 18)° + (9x - 27)°

99° = 3x + 9x + 18° - 27°

99° = 12x - 9°

12x = 99° + 9°

12x = 108°

x = 108/12

x = 9°

Now, angle PSQ = 3(9°) + 18°

= 27° + 18°

= 45°

Therefore, the measure of PSQ in degrees is 45°.

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What is the measure of PSQ in degrees? Angle PSR measures 99°.

Summary:

Angle PSR measures 99°, then the measure of angle PSQ in degrees is 45°.