Question

n circle A shown below, m Arc BC is 61° and m Arc EF is 76°: Points B, C, E, F lie on Circle A. Lines BE and CF pass through point D creating angle EDF. Measure of arc BC is 61 degrees and What is m∠FDE?

Answer 1

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

Answer:

The correct answer is 68.5°

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°

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