Question

What are the measures of angles P and S? ∠P = 20°; ∠S = 160° ∠P = 40°; ∠S = 140° ∠P = 140°; ∠S = 40° ∠P = 160°; ∠S = 20°

Answer 1

*see attachement for diagram

Answer:

∠P = 140°; ∠S = 40°

Step-by-step explanation:

The figure given is a parallelogram.

Consecutive angles (adjacent angles) of a parallelogram are supplementary.

Therefore:

(x + 15)° + (6x - 10)° = 180°

Solve for x

x + 15 + 6x - 10 = 180

Add like terms

7x + 5 = 180

7x = 180 - 5

7x = 175

x = 175/7

x = 25

✔️m<P = m<R = 6x - 10 (opposite angles of a parallelogram are congruent)

m<P = 6x - 10

Plug in the value of x

m<P = 6(25) - 10 = 140°

✔️m<S = m<Q = x + 15 (opposite angles of a parallelogram are congruent)

m<S = x + 15 = 25 + 15 = 40°