Question

∠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?

Answer 1

260................................................

Answer 2

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°.