Question

(iv) Observe the figure, ZPQR and PTR are inscribed in the arc PQR and they intercept arc PMR. If ZPQR = 85°, then find the measure of ZPTR. Give reason. 9
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Answer 1

Answer:

SSC (Marathi Semi-English) 10th Standard [इयत्ता १० वी]

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Sum

Prove that, angles inscribed in the same arc are congruent.

Given: ∠PQR and ∠ PSR are inscribed in the same arc

Arc PXR is intercepted by the angles.

To prove: ∠ PQR ≅ ∠ PSR

Proof :

m∠PQR =

12 m(arc PXR) ...(i) ______________

m∠________ =

12 m(arc PXR) ....(ii) ____________

∴ m∠ ________ = m∠PSR ....[From (i) and (ii)]

∴ ∠ PQR ≅ ∠ PSR ....(Angles equal in measure are congruent)