Question

In the figure given below, P and Q are centres of two circles, intersecting at B and C, and ACD is a straight line.

If ∠APB = 150° and ∠BQD= x, find the value of x
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Answer 1

Answer:

The angle subtended by an arc of a circle at its centre is twice the angle subtended by the same arc at a point on the circumference

So we get

∠APB=2∠ACB

It can be written as

∠ACB=/2∠APB

By substituting the values

∠ACB=150/2

so we get

∠ACB= 75°

We know that ACD is a straight line

It can be written as

∠ACB+∠DCB=180°

By substituting the values

75 +∠DCB=180°

On further calculation

∠DCB=180° −75

By subtraction

∠DCB=105°

We know that

∠DCB=1/2×reflec ∠BQD

By substituting the values

105° =1/2×(360°-x)

On further calculation

210° =36° −x

By subtraction

x=105°

Therefore, the value of x is 150°