Question

In the adjoining figure, ZPOQ is a straight line. If ZPOR=45° and ZSOQ=52°, find the measure of ZROS.​

Answer 1

Answer:

lnΔPRT

∠RPT+∠PRT+∠RTP=180

∘

(angle sum property of a triangle)

⇒95

∘

+40

∘

+∠RTP=180

∘

⇒135

∘

+∠RTP=180

∘

⇒∠RTP=180

∘

−135

∘

=45

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Now ∠RTP=∠STQ=45

∘

(vertically opposite angles)

lnΔSTQ

∠STQ+∠TSQ+∠SQT=180

∘

(angle sum property of a triangle)

⇒45

∘

+75

∘

+∠SQT=180

∘

⇒∠SQT=180

∘

−(45

∘

+75

∘

)

=180

∘

−120

∘

=60

∘

Hence, ∠SQT=60

∘

Step-by-step explanation:

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