Question

in the diagram below, find the value of x.
answer attempt 1 out of 2
additional solution no solution
x = submit answer

Explanation:

Step1: Use the inscribed - angle theorem

The inscribed - angle theorem states that an inscribed angle is half of the central angle subtended by the same arc. Here, the arc \(WY\) is subtended by the inscribed angle \(\angle WXY = 5x^{\circ}\) and the central angle (in this case, since \(WY\) is a diameter, the central angle is \(180^{\circ}\)).

Step2: Set up the equation

We know that \(5x=\frac{1}{2}\times180\).
Simplify the right - hand side of the equation: \(\frac{1}{2}\times180 = 90\). So, \(5x=90\).

Step3: Solve for \(x\)

Divide both sides of the equation \(5x = 90\) by \(5\). Using the formula \(x=\frac{90}{5}\).

Answer:

\(x = 18\)