Question

Circle E, and are diameters. Angle BCA measures 53°.

Circle E is shown. Line segments A C and B D are diameters. Lines are drawn to connect points B and C and points A and D. Angle B C A is 53 degrees.

What is the measure of arc AD?

53°
74°
106°
180°

Answer 1

The answer is B on Edge 2020`

Explanation:

I did the exam

Answer 2

74°

Explanation:

see the attached figure to better understand the problem

we know that

Triangle EBC is an isosceles triangle (because has two equal sides EB=EC)

so

`m\angle BCA=m\angle BCE=m\angle EBC=53^o`

Find the measure of angle BEC

Remember that the sum of the interior angles in any triangle must be equal to 180 degrees

so

`m\angle BCE+m\angle EBC+m\angle BEC=180^o`

substitute the given values

`53^o+53^o+m\angle BEC=180^o`

`m\angle BEC=180^o-106^o=74^o`

Find the measure of angle AED

we know that

`m\angle AED=m\angle BEC` ----> by vertical angles

so

`m\angle AED=74^o`

Find the measure of arc AD

we know that

`m\ arc\ AD=m\angle AED` -----> by central angle

therefore

`m\ arc\ AD=74^o`