Question

in the diagram below, ⊙o is circumscribed about quadrilateral defg. what is the value of x? a. 68° b. 62° c. 90° d. 112°

Explanation:

Step1: Recall cyclic - quadrilateral property

Opposite angles of a cyclic quadrilateral are supplementary (their sum is 180°).

Step2: Identify opposite angles

In cyclic quadrilateral DEFG, ∠E and ∠G are opposite angles.

Step3: Set up the equation

We know that ∠E = 112° and ∠G=x°. So, ∠E+∠G = 180°.
112°+x° = 180°

Step4: Solve for x

x=180 - 112
x = 68°

Answer:

A. 68°