Question

In circle A shown below, m arc BC is 61° and m Arc EF is 76°.

What is m∡FDE?
Answer
76°
38°
30.5°
68.5°

Answer 1

68.5°

Explanation:

Here is the solution:

m<FDE = 1/2( Arc BC + Arc 76)
m<FDE = 1/2 (61° + 76°)
m<FDE = 137/2 = 68.5°

So the answer is 68.5°

Answer 2

The correct answer among the choices provided is the fourth option. The calculated result of the angle FDE is 68.5°. Whenever two chords cut across a circle, the resulting angle is equivalent to half of the sum of the measurements of the arc the angle intersects and that which the angle vertical to the first angle intercepts.
m<FDE = 1/2( Arc BC + Arc 76)
m<FDE = 1/2 (61° + 76°)
m<FDE = 137/2 = 68.5°