m∠R = 110° and m∠S = 110°
Solution:
Given data:
RSWY is a parallelogram.
∠R = (5x – 90)° and ∠S = (2x + 30)°
In RSWY, ∠R and ∠S are opposite angles.
Opposite angles of a parallelogram are congruent.
m∠R = m∠S
(5x – 90°) = (2x + 30)°
5x° – 90° = 2x° + 30°
Add 90° on both sides of the equation, we get
5x° = 2x° + 120°
Subtract 2x° on both sides of the equation, we get
3x° = 120°
Divide by 3 on both sides of the equation.
x° = 40°
Substitute x = 40 in m∠R and m∠S.
m∠R = (5x – 90)°
= 5(40°) – 90°
m∠R = 110°
m∠S = (2x + 30)°
= 2(40°) + 30°
m∠S = 110°
Hence m∠R = 110° and m∠S = 110°.
