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Marizza181 [45]
3 years ago
13

∠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?

Mathematics
2 answers:
mestny [16]3 years ago
7 0
260................................................
kicyunya [14]3 years ago
6 0

Answer: The measure of ∠BEC = 50°.

Step-by-step explanation:

Since we have given that

∠BEC is formed inside a circle by two intersecting chords.

and the value of minor arc BD = 94

The value of major arc CA = 166

We need to find the measure of ∠ BEC.

As we know theorem, the angle AEC is equal to half the sum of the intercepted arcs.

We will use to  find the intercepted angles when two chords got intersected i.e.

m\angle AEC=\frac{\text{ Minor arc+ Major arc}}{2}\\\\m\angle AEC=\frac{94+166}{2}\\\\m\angle AEC=\frac{260}{2}\\\\m\angle AEC=130^\circ

Since ∠ AEC and ∠BEC are supplementary angles.

So, it becomes,

\angle AEC+\angle BEC=1806\circ\\\\ 130^\circ+\angle BEC=180\circ\\\\\angle BEC=180^\circ-130^\circ=50^\circ

Hence, the measure of ∠BEC = 50°.

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