Question

in circle F, points A,B,C,D, and E are located on the circle such that measure of C=119°, and BE is perpendicular AD. determine the measure of arc AE. show how you arrived at your answer.

Answer 1

Measure of arc AE = 58°

Explanation:

As shown: ABCD is a quadrilateral, ∠C = 119°

So, ∠C + ∠A = 180°

∴ ∠A = 180° - ∠C = 180° - 119° = 61°

ΔAGB is a right triangle at G

So, ∠A + ∠B = 90°

∴ ∠ABG = 90 - ∠A = 90 - 61 = 29°

Arc AE opposite to the angle ∠ABG

So, measure of arc AE = 2∠ABG = 2 * 29° = 58°