Question

question 10 of 10
in the diagram below, ⊙o is circumscribed about quadrilateral abcd. what is the value of x?

Explanation:

Step1: Recall property of cyclic quadrilateral

Opposite angles of a cyclic quadrilateral are supplementary, i.e., they add up to 180°. Here, ∠B and ∠D are opposite angles. So, 80°+2x° = 180°.

Step2: Solve the equation for x

Subtract 80 from both sides of the equation 80 + 2x=180. We get 2x=180 - 80, so 2x = 100. Then divide both sides by 2: $x=\frac{100}{2}=50$.

Answer:

C. 50