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in Plane Geometry and Line and Angle by (35.3k points)
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In the given figure, ∠PQR = ∠PRQ then prove that ∠PQS = ∠PRT.

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by (34.1k points)
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Best answer

We are given that 

∠PQR = ∠PRQ ,..(i)

From figure,

∠PQS + ∠PQR = 180°

(linear pair axiom) …(ii)

and ∠PRT + ∠PRQ = 180°

(linear pair axiom) …(iii)

Using (ii) and (iii)

∠PQS + ∠PQR = ∠PRT + ∠PRQ

Again using (i) i.e. ∠PQR = ∠PRQ, we get

⇒ ∠PQS = ∠PRT

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