Question

angle qps is equal to 2 angle SPR, angle q angle r + 40 degree and angle PSR is equal to 120 degree find qPR​

Answer 1

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