Question

quadrilateral pqrs is inscribed in a circle where PS is a diameter and angle pqr is equal to 140 degree. find angle SPR

Answer 1

Step-by-step explanation:

Correct option is

B

60

∘

PQRS is a cyclic quadrilateral.

Then, ∠PQR+∠PSR=180

∘

...[Opposite angles of cyclic quadrilateral are supplementary]

⟹ ∠PQR+150

o

=180

∘

⟹ ∠PQR=180

∘

−150

∘

=30

∘

.

In △PQR,

∠PRQ=90

∘

(Angle of a semicircle)

Then, ∠RPQ+90

∘

+30

∘

=180

∘

...[Angle sum property]

⇒∠RPQ+120

∘

=180

∘

⇒∠RPQ=60

∘

.

Hence, option B is correct