Question

In the diagram below O is circumscribed about quadrilateral DEFG. What is the value of x

Answer 1

Answer:

Option D

68 degrees is the answer.

Step-by-step explanation:

In the picture there is a quadrilateral DEFG and a circle circumscribing the quadrilateral.

In other words, DEFG is a cyclic quadrilateral.

We know that in cyclic quadrilateral, opposite angles are supplementary.

Hence in the given quadrilateral, Angles D and F are supplementary and also the pair E and G are supplementary.

Angle G is x and we have to find x.

Sum of angles G and E = 180  degrees (since they are supplementary)

Angle E = 112 degrees (given)

Hence angle G = x = 180-112 = 68 degrees.

Answer 2

Answer C. 68

Step-by-step explanation: