Question

Quadrilateral ABCD is inscribed. The measure of ZA = 67º. What is the measure of ZC?

Answer 1

m<C = 113°

Explanation:

m<A = 67° (given)

Recall: opposite angles in any inscribed quadrilateral in a circle are equal to 180° or are supplements of one another.

This implies that:

m<A + m<C = 180°

Substitute

67° + m<C = 180°

Subtract 67° from each side

m<C = 180° - 67°

m<C = 113°