measure of angle ACE given intercepted arcs
Check the final answer first, then review the worked steps.
Problem
measure of angle ACE given intercepted arcs
Step-by-step solution
The angle ACE is formed by two secants intersecting outside the circle. The measure of the angle is half the difference of the intercepted arcs. The intercepted arcs are arc AE and arc BD. Arc AE is given as 106 degrees. Arc BD is given as 48 degrees. So, $\angle ACE = \frac{1}{2} (m(\text{arc } AE) - m(\text{arc } BD)) = \frac{1}{2} (106^\circ - 48^\circ) = \frac{1}{2} (58^\circ) = 29^\circ$.
Answer
29°