Question

Quadrilateral EFGH is inscribed in a circle. If m∠F = 114° and m∠G = 78° then which of the following is the measure of ∠H?

Answer 1

m∠H=66°

Explanation:

Since Quadrilateral EFGH is inscribed in a circle, it is a Cyclic quadrilateral.

Theorem: Opposite Angles of a Cyclic Quadrilateral are Supplementary.

Angles F and H are opposite angles of a cyclic quadrilateral and by the theorem above:

m∠F+m∠H=180 degrees

114° +m∠H=180°

m∠H=180° - 114°

m∠H=66°