Respuesta :

Answer : C. 75°

Given : arc length AC=110, CB=20, AD=190, and BD=40

We need to find ∠AEC

The below is the formula for measure of an angle formed by two chords

∠AEC = [tex] \frac{1}{2} ( arc AC + arcBD) [/tex]

We know arc AC = 110 and arc BD = 40

So ∠AEC = [tex] \frac{1}{2} ( 110 + 40) [/tex]

= [tex] \frac{150}{2} = 75 [/tex]

∠AEC = 75 degrees

Answer:

C. 75°

Step-by-step explanation:

We have been given a circle and we are asked to find the measure of angle AEC.

We will use Intersecting chords theorem to find the measure of angle AEC, which states that measure of angle formed inside a circle by two intersecting chords is one half the sum of the measure of the arcs intercepted by the angle and its vertical angle.

We can see that measure of arc AC is 110 degrees and measure of its vertical arc BD is 40 degrees.

[tex]m\angle AEC=\frac{110^o+40^o}{2}[/tex]

[tex]m\angle AEC=\frac{150^o}{2}[/tex]

[tex]m\angle AEC=75^o[/tex]

Therefore, measure of angle AEC is 75 degrees and option C is the correct choice.

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