If the sum of a central angle and an inscribed angle of a circle is 180°, then what is the measure of the central angle?

Q.If the sum of a central angle and an inscribed angle of a circle is 180°, then what is the measure of the central angle?

Let the measure of the central angle be \(x\). \(\therefore\) The inscribed angle will be \(\frac{x}{2}\) \(\therefore x + \frac{x}{2} = 180^\circ\) i.e., \(\frac{3x}{2} = 180^\circ\) i.e., \(x = 180^\circ \times \frac{2}{3}\) i.e., \(x = 120^\circ\) \(\therefore\) The measure of the central angle is \(120^\circ\)