Answer:
x=15°
Step-by-step 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°
