In the diagram below, quadrilateral L, M, N, OLMNO is inscribed in circle PP. Find the measure of angle, O∠O.

P
L
M
N
O
99°
116°

1 answer

Inscribed angles that intercept the same arc are equal in measure. Since angles L, M, and N all intercept the same arc (arc LMN), we can determine the measure of angle O by subtracting the sum of angles L, M, and N from 360 degrees (the measure of a full circle):

∠O = 360° - (99° + 116° + 116°)
∠O = 360° - 331°
∠O = 29°

Therefore, the measure of angle O, ∠O, is 29 degrees.