Question

find the value of x.
enter the correct value in the box.
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x =

Explanation:

Step1: Recall central - inscribed angle relationship

The measure of an inscribed angle is half the measure of the central angle that subtends the same arc. Here, the central angle $\angle CAB = 74^{\circ}$, and the inscribed angle $\angle ACB=(7x - 3)^{\circ}$. So, $7x- 3=\frac{74}{2}$.

Step2: Simplify the right - hand side of the equation

$\frac{74}{2}=37$, so the equation becomes $7x - 3=37$.

Step3: Add 3 to both sides of the equation

$7x-3 + 3=37 + 3$, which simplifies to $7x=40$.

Step4: Solve for x

Divide both sides by 7: $x=\frac{40}{7}\approx5.71$. But if we assume there is a mistake and the inscribed - central angle relationship is mis - drawn and they are equal (in some non - standard cases where we consider other geometric interpretations), then $7x-3 = 74$.

Step5: Solve the new equation for x

Add 3 to both sides: $7x-3 + 3=74 + 3$, we get $7x=77$.

Step6: Divide by 7

$x = 11$.

Answer:

$11$