Question

EFGH is a quadrilateral inscribed in circle P with the measure of angle E = 72 and the measure of angle F = 49. Find the measure of angle H.

Answer 1

131°

Explanation:

An inscribed quadrilateral is any four sided shape enclosed by a circle with vertices on the the circumference of a circle. This results in a relationship between the opposite angles of the quadrilateral. It states that the sum of the opposite angles of such quadrilateral is equal to 180°.

The quadrilateral EFGH has ∠ E, ∠F, ∠G and ∠H. ∠ E and ∠G are opposite to each other while ∠ F and ∠H are opposite to each other.

Therefore, ∠F + ∠H = 180

∠H = 180 - ∠F

∠H = 180 - 49 = 131

∠H = 131°