Question

In the figure below, \overline{AB}

Answer 1

Answer:

Arc AD = 43°

Step-by-step explanation:

Image is attached.

When an angle subtends from an Arc to the center, the measure of the Arc and the Angle are same. Now, looking at the figure,

Arc AB = 180 (since this is an Arc subtending the diameter)

Arc DC = 90 degrees since the central angle is 90

So,

Arc AD + Arc CB = 180 - 90 = 90

Arc AD and Arc CB have the same measures as the central angle it created (terms in x). So we can write:

Arc AD + Arc CB = 90

7x + 1 + 9x - 7 = 90

We can solve for x:

$7x + 1 + 9x - 7 = 90\\16x-6=90\\16x=96\\x=6$

The central angle AD is:

AD = 7x + 1 = 7(6) + 1 = 43

Also, Arc AD is same, thus:

Arc AD = 43°