Question

∠BEC is formed inside a circle by two intersecting chords. If minor arc BD = 94 and minor arc AC = 166, what is the measure of ∠ BEC? A) 44° B) 47° C) 50° D) 53°

Answer 1

The answer is 50

Explanation:

bc its just right idk how but it is

Answer 2

∠BEC = 50°

Explanation:

For better understanding of the solution, see the attached figure of the problem :

Minor arc BD = 94

Minor arc AC = 166

Now, the angle formed by the intersection of the two chords is ∠BED

And, the angle formed by the intersection of two chords is half the sum of angle measures of the corresponding chords.

`\implies \angle BED =(1)/(2)* (BD + AC)\\\\ \implies \angle BED = (1)/(2)* (94+166)\\\\\implies \angle BED=(1)/(2)* 260\\\\\implies\angle BED = 130`

Now, ∠BED + ∠BEC = 180 ( Adjacent angles )

⇒ ∠BEC = 180 - 130

⇒ ∠BEC = 50°