Question

In the figure, the measure of arc DE = 124° and the measure of arc BC = 36°. The diagram is not drawn to scale.

(picture attached below)

What is the measure of ∡A?
Answer Choices:
A. 44°
B. 62°
C. 80°
D. 88°

thank you so much in advance! :)

Answer 1

The answer is 44 degrees

Answer 2

The measure of angle ∠A is 44°

Explanation:

Given the measure of angles in the figure

measure of arc DE=124° and arc BC=36°

we have to find the measure of ∠A

By the theorem of intercepted arcs to the angle of two secants which states that

The measure of an angle formed by the two secants from a point outside the circle is half the difference of the intercepted arcs i.e

`m \angle A=(1)/(2)(arc DE-arc BC)`

`\angle A=(1)/(2)(\angle DOE-\angle BOC)`

`\angle A=(1)/(2)(124^(\circ)-36^(\circ))=(1)/(2)* 88=44^(\circ)`

The measure of angle ∠A is 44°

Option A is correct.