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Question
In the figure if ∠PQR = 50°, then find ∠PSR.
Solution
In given figure,
∠PQR ≅ ∠PSR ......[Angles inscribed in the same arc are congruent]
∴ ∠PSR = 50°
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Given: ∠PQR and ∠PSR are inscribed in the same arc
Arc PXR is intercepted by the angles.
To prove: ∠PQR ≅ ∠PSR
Proof :
m∠PQR = `1/2` m(arc PXR) .......(i) `square`
m∠`square` = `1/2` m(arc PXR) ......(ii) `square`
∴ m∠`square` = m∠PSR .......[From (i) and (ii)]
∴ ∠PQR ≅ ∠PSR ........(Angles equal in measure are congruent)
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