Question

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

Explanation:

Step1: Recall circle - angle property

The measure of an inscribed - angle is half the measure of its intercepted arc. Here, if the inscribed - angle is \((9x - 2)^{\circ}\) and the central - angle (which is equal to the measure of the intercepted arc) is \((15x + 20)^{\circ}\), we know that the central - angle is twice the inscribed - angle. So, \(15x+20 = 2(9x - 2)\).

Step2: Expand the right - hand side

Expand \(2(9x - 2)\) to get \(18x-4\). So the equation becomes \(15x + 20=18x-4\).

Step3: Move like terms together

Subtract \(15x\) from both sides: \(20=18x - 15x-4\), which simplifies to \(20 = 3x-4\). Then add 4 to both sides: \(20 + 4=3x\), or \(24 = 3x\).

Step4: Solve for \(x\)

Divide both sides of the equation \(24 = 3x\) by 3. We get \(x=\frac{24}{3}=8\).

Answer:

8