Question

question 9 of 10
in the diagram below, ⊙p is circumscribed about quadrilateral abcd. what is the value of x?
a. 60°
b. 120°
c. 100°
d. 80°

Explanation:

Step1: Recall cyclic - quadrilateral property

In a cyclic quadrilateral (a quadrilateral circum - scribed about a circle), the sum of opposite angles is 180°.

Step2: Identify opposite angles

Angle B and angle D are opposite angles in cyclic quadrilateral ABCD. Given angle B = 100°.

Step3: Set up the equation

Let angle D=x. Then, using the property of cyclic quadrilaterals, we have ∠B+∠D = 180°. Substituting the value of ∠B, we get 100°+x = 180°.

Step4: Solve for x

Subtract 100° from both sides of the equation: x=180° - 100° = 80°.

Answer:

D. 80°