Question

in the diagram below, ⊙o is circumscribed about quadrilateral defg. what is the value of x? e 119° 90° f a. 61° b. 59° c. 90° d. 119°

Explanation:

Step1: Recall cyclic - quadrilateral property

Opposite angles of a cyclic quadrilateral are supplementary (sum to 180°). Angle E and angle G are opposite angles in the cyclic quadrilateral DEFG.

Step2: Set up the equation

We know that ∠E+∠G = 180°. Given ∠E = 119°, we substitute into the equation: 119°+x = 180°.

Step3: Solve for x

Subtract 119° from both sides of the equation: x=180° - 119°. So, x = 61°.

Answer:

A. 61°