Question

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what is the measure of $overset{\frown}{ac}$?
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$square^circ$
$(4x + 17)^circ$
$(4x - 3.5)^circ$

Explanation:

Step1: Relate arc and inscribed angle

The measure of an inscribed angle is half the measure of its intercepted arc. So:
$$(4x - 3.5) = \frac{1}{2}(4x + 17)$$

Step2: Solve for x

Multiply both sides by 2:
$$2(4x - 3.5) = 4x + 17$$
$$8x - 7 = 4x + 17$$
Subtract $4x$ from both sides:
$$4x - 7 = 17$$
Add 7 to both sides:
$$4x = 24$$
$$x = 6$$

Step3: Calculate arc $\overparen{AC}$

Substitute $x=6$ into $(4x + 17)$:
$$4(6) + 17 = 24 + 17$$

Answer:

$41^\circ$