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?

Answer 1

The value of ∠BEC is 50°

Minor arc BD = 94° (Given)

Minor arc AC = 166° (Given)

Angle formed by intersecting two chords = ∠BED

Therefore,

∠BED  = 1/2 × ( BD + AC)

∠BED  = 1/2 × ( 94 + 166 )

∠BED  = 1/2 × 260

∠BED  = 130

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

∠BEC = 180 - 130

∠BEC = 50°

Therefore, the value of ∠BEC is 50°