m∠QPS=40 ∘ m, angle, Q, P, S, equals, 40, degrees \qquad m \angle RPS = 8x + 7^\circm∠RPS=8x+7 ∘ m, angle, R, P, S, equals, 8, x, plus, 7, degrees \qquad m \angle QPR = 9x + 16^\circm∠QPR=9x+16 ∘ m, angle, Q, P, R, equals, 9, x, plus, 16, degrees Find m\angle QPRm∠QPRm, angle, Q, P, R:
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The correct formatted question is,
m∠QPS=40°, m∠RPS=8x+7°, m∠QPR=9x+16°. Find m∠QPR.
Consider the attached figure, while going through the following steps:
Given,
∠ QPS = 40°
∠ RPS = 8x + 7°
∠ QPR = 9x + 16°
From figure it's clear that,
∠ QPS = ∠ QPR + ∠ RPS
40° = 9x + 16° + 8x + 7°
40° = 17x + 23°
17x = 40° - 23°
17x = 17°
∴ x = 1°
Now, we need to find ∠ QPR
∠ QPR = 9x + 16°
= 9 (1°) + 16°
= 9° + 16°
= 25°
∴ ∠ QPR = 25°
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