Question

find the value of x.
148°
x = ?°

Explanation:

Step1: Find the measure of the arc opposite to angle \( y \)

The measure of an inscribed angle \( y \) is half the measure of its intercepted arc. The arc intercepted by \( y \) is \( 148^{\circ} \), so \( y=\frac{148^{\circ}}{2} = 74^{\circ}\).

Step2: Use the property of a semicircle

Since \( x + y=90^{\circ}\) (angle in a semicircle), and \( y = 74^{\circ}\), then \( x=90^{\circ}-y\).
Substitute \( y = 74^{\circ}\) into the equation: \( x=90^{\circ}-74^{\circ}\).

Answer:

\(16\)