angle qps is equal to 2 angle SPR, angle q angle r + 40 degree and angle PSR is equal to 120 degree find qPR
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Answer:
120⁰
Step-by-step explanation:
‹PSQ = 180⁰ - ‹PSR = 180⁰ - 120⁰ = 60⁰
In ∆PQS
‹QPS + ‹Q + ‹PSQ = 180⁰
Use ‹QPS = 2‹SPR and ‹Q = ‹R + 40⁰
2‹SPR + ‹R + 40⁰ + 60⁰ = 180⁰. (Given values used)
2‹SPR + ‹R = 100⁰. (1)
In ∆SPR
‹SPR + ‹R + ‹PSR = 180⁰
‹SPR + ‹R + 120⁰ = 180⁰
‹SPR + ‹R = 60⁰. (2)
Subtract (2) from (1)
‹SPR = 40⁰
‹QPS = 2‹SPR = 2*40⁰ = 80⁰
‹QPR = ‹QPS + ‹SPR = 80⁰ + 40⁰ = 120⁰
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