Question

Given

\qquad m \angle QPS = 47^\circm∠QPS=47 ∘

m, angle, Q, P, S, equals, 47, degrees

\qquad m \angle RPS = 3x - 38^\circm∠RPS=3x−38 ∘

m, angle, R, P, S, equals, 3, x, minus, 38, degrees

\qquad m \angle QPR = 7x - 95^\circm∠QPR=7x−95 ∘

m, angle, Q, P, R, equals, 7, x, minus, 95, degrees

Find m\angle QPRm∠QPRm, angle, Q, P, R:

Answer 1

Given : m∠QPS = 47°

m∠RPS = 3x - 38°

m∠QPR = 7x - 95°

To Find : m∠QPR

Solution:

∠QPS = ∠RPS + ∠QPR

m∠QPS =m ∠RPS + m∠QPR

=> 47° = 3x - 38° + 7x - 95°

=> 47° = 10x - 133°

=> 10x  = 47° +  133°

=> 10x  =180°

=> x = 18°

m∠QPR = 7x - 95°

= 7(18°) - 95°

=  126° - 95°  

= 31°

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