In the figure below, \overline{AB}
AB
start overline, A, B, end overline is a diameter of circle PPP.
What is the arc measure of \stackrel{\LARGE{\frown}}{AD}
AD
⌢
A, D, start superscript, \frown, end superscript in degrees?

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:

The central angle AD is:

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

Also, Arc AD is same, thus:

Arc AD = 43°

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step-by-step explanation:

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