Question

POQ is a straight line and OS stands on PQ. Find the value of x and the measure of ∠POS, ∠SOR and ∠ROQ.

Answer 1

Answer:

x=19, ∠POS=99°, ∠SOR=17°,∠ROQ=64°

Step-by-step explanation:

POQ is a straight line

∠POS+∠SOR+∠ROQ=180°

(5x+4)+(x-2)+(3x+7)=180°

5x+4+x-2+3x+7=180°

5x+x+3x+4-2+7=180°

9x+9°=180°

9x=180°-9°

9x=171°

x=171°/9

x=19°

∠POS=5x+4=5(19°)+4=95°+4=99°, ∠SOR=x-2=19°-2=17°,

∠ROQ=3x+7=3(19°)+7=57°+7=64°.

Therefore, the value of x is 19° and the measure of ∠POS, ∠SOR and ∠ROQ is 99°, 17° and 64°.