Question

3) In the figure, QR is the diameter of the semicircle.
a) What is the measure of angle PQS ?
b) What is the measure of angle QSR ?
c) What is the measure of < SPQ ?
d) What is the measure of ZPRQ ?
PQ = QR, Z RQS = 40⁰.
​

Answer 1

Answer:

RULES MEASURING ANGLE SUM PROPERTY CONSTRUCTION

Step-by-step explanation:

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.