Question

Angle ABD measures (4x + 10)o. Angle ACD measures (5x − 2)o.

Circle E is shown. Angles A B D and A C D intercepts arc A D. Angles B A C and B D C intercepts arc B C.

What is the measure of arc AD?
12°
58°
96°
116°

Answer 1

Answer: 116

Step-by-step explanation:

Answer 2

The measure of arc AD is 116 degrees

Circle geometry

Using the theorem that, angle at the same segment are equal, hence;

4x + 10 = 5x - 2

4x  - 5x = -2-10
x = 12

The measure of arc is expressed as:

arcAD = 4x + 10 + 5x - 2

arcAD = 4(12) + 10 + 5(12) - 2
arcAD - 48 + 10 + 60 -2
arcAD = 116 degrees

Hence the measure of arc AD is 116 degrees

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