Question

c is the centre of a circle passing through the points p,q,r,s and angle psr is 120.pq is a diameter then find angle qpr

Answer 1

Answer:

30°

Step-by-step explanation:

Let us draw a circle pqrs with center at c and pq as diameter (See the attachment). It is given that ∠psr=120°.

Now we have to find the value of ∠qpr.

Assume that, ∠prs=x, ∠spr=y and ∠qpr=A.

Since pq is a diameter, so, ∠prq=90°.

Now, take Δpsr where,

∠prs+ ∠spr+ ∠psr=180°

⇒ y+x+120°=180°

⇒x+y=60° ....... (1)

Again, we have that the sum of opposite angles of a cyclic quadrilateral is  180°.

So, using this property, we can write,

∠spq+ ∠srq = 180°

⇒(A+x)+(y+90°)=180°

⇒A= 180°-90°-(x+y)

⇒A= 90°-60° {From the equation (1)

⇒A= 30°

⇒∠qpr = 30° (Answer)