∠BEC is formed inside a circle by two intersecting chords. If minor arc BD = 94 and minor arc CA = 166, what is the measure of

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25-05-2018
Mathematics

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∠BEC is formed inside a circle by two intersecting chords. If minor arc BD = 94 and minor arc CA = 166, what is the measure of

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calculista calculista · Answer 1 · 2018-06-06T15:06:49+02:00

the complete question is
∠BEC is formed inside a circle by two intersecting chords. If minor arc BD = 94 and minor arc CA = 166, what is the measure of ∠ BEC?

the picture in the attached figure

we know that
The angle formed inside of a circle by two intersecting chords is the half-summit of the arcs that comprise it and its opposite.
so
∠BED=(1/2)*[arc AC+arc BD]-----> (1/2)*[166+94]-----> 130°
∠BEC+∠BED=180°-----> by supplementary angles
∠BEC=180-130-----> 50°

the answer is
∠BEC=50°