Q. 195.0( 1 Vote )

*PQRS* is a cyclic quadrilateral such that *PR* is a diameter of the circle. If ∠*QPR*=67° and ∠*SPR*=72°, then ∠*QRS*=

A. 41°

B. 23°

C. 67°

D. 18°

Answer :

Given that,

PQRS is a cyclic quadrilateral

∠QPR =67°

∠SPR = 72°

∠SPQ = ∠QPR + ∠SPR

= 67^{o} + 72^{o}

= 139°

∠SPQ + ∠QRS = 180° (Opposite angles of cyclic quadrilateral)

139^{o} + ∠QRS = 180°

∠QRS = 41°

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