Math, asked by minhajurrehman24, 7 months ago

2. In figure 3.57, PQRS is cyclic.
side PQ=side RQ. ZPSR = 110°, Find-
(1) measure of Z POR
(2) m(arc PQR)
(3) m(arc QR)
(4) measure of Z PRO

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Answers

Answered by aadityamishra2970

Step-by-step explanation:

PQRS is a cyclic quadrilateral. [Given] ∴ ∠PSR + ∠PQR = 180° [Opposite angles of a cyclic quadrilateral are supplementary] ∴ 110° + ∠PQR = 180° ∴ ∠PQR = 180° – 110° ∴ m ∠PQR = 70° ii. ∠PSR= 1/2 m (arcPQR) [Inscribed angle theorem] 110°= 1/2 m (arcPQR) ∴ m(arc PQR) = 220° iii. In ∆PQR, side PQ ≅ side RQ [Given] ∴ ∠PRQ = ∠QPR [Isosceles triangle theorem] Let ∠PRQ = ∠QPR = x Now, ∠PQR + ∠QPR + ∠PRQ = 180° [Sum of the measures of angles of a triangle is 180°] ∴ ∠PQR + x + x= 180° ∴ 70° + 2x = 180° 2x = 180° – 70° ∴ 2x = 110° ∴ x = 100°/2 = 55° ∴ ∠PRQ = ∠QPR = 55°….. (i) But, ∠QPR = 1/2 nm(arc QR) [Inscribed angle theorem] ∴ 55° = 1/2 m(arc QR) ∴ m(arc QR) = 110° iv. ∠PRQ = ∠QPR =55° [From (i)] ∴ m ∠PRQ = 55°

Answered by yadavmuskanyadav702

Answer:

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