The angles in a quadrilateral PQRS are such that angle S is fourth proportional of angles P, Q and R. If the ratio of angles Q and P is 5 : 4, and angle S is 125°, find the measure of angle R.
1). 90°
2). 100°
3). 108°
4). 120°
Angle S is fourth proportional of angles P, Q and R.
⇒ P/Q = R/S
Ratio of angles Q and P is 5 : 4, and angle S is 125°.
So, P/Q = 4/5
⇒ 4/5 = R/125
⇒ R = 4 × 25 = 100
∴ Measure of angle R is 100°.