In the diagram, O is the center of the circle, If ?POQ = 80o and ?PRQ = 5x, find the value of x.

In the diagram, O is the center of the circle, If ?POQ = 80^o and ?PRQ = 5x, find the value of x.

Answer Details

In a circle, the angle subtended by an arc at the center is twice the angle subtended by the same arc at any point on the circumference of the circle. Using this property, we can find the value of ?PRQ: ?POQ = 80^o (given) Therefore, ?PRQ = 1/2 ?POQ = 1/2 x 80^o = 40^o Now, we can use the value of ?PRQ to find the value of x: ?PRQ = 5x (given) Substituting the value of ?PRQ, we get: 40^o = 5x Simplifying this equation, we get: x = 8 Therefore, the value of x is 8. The answer is option B.