Question

Given: circle k(O)

m∠OFQ = 52°, m FQ = (5x+1)

Find: x

Answer 1

x=15°

Explanation:

step 1

Find the measure of arc QD

we know that

The inscribed angle is half that of the arc it comprises.

so

m∠OFQ=(1/2)[arc QD]

substitute the given value

52°=(1/2)[arc QD]

104°=[arc QD]

arc QD=104°

step 2

Find the value of x

Remember that the diameter divide the circle into two equal parts

so

arc FQ+arc QD=180°

we have

arc QD=104°

arc FQ=(5x+1)°

substitute

(5x+1)°+104°=180°

5x=180°-105°

x=15°