To determine the measure of an inscribed angle when the measure of its intercepted arc is given, we can use a fundamental property from circle geometry.
An inscribed angle in a circle is always half the measure of its intercepted arc. This property is crucial for solving the problem.
Given:
- The measure of the intercepted arc is [tex]\(124^\circ\)[/tex].
Following the property, to find the measure of the inscribed angle, we divide the measure of the intercepted arc by 2.
Step-by-step solution:
1. Start with the measure of the intercepted arc: [tex]\(124^\circ\)[/tex].
2. Use the inscribed angle property: Inscribed angle [tex]\( = \frac{1}{2} \times \text{measure of the intercepted arc}\)[/tex].
3. Substitute the intercepted arc measure into the formula: Inscribed angle [tex]\( = \frac{1}{2} \times 124^\circ\)[/tex].
4. Perform the division: [tex]\(\frac{124}{2} = 62\)[/tex].
Thus, the measure of the inscribed angle is [tex]\(62^\circ\)[/tex].
Among the given options:
- [tex]\(124^\circ\)[/tex]
- [tex]\(62^\circ\)[/tex]
- [tex]\(31^\circ\)[/tex]
- [tex]\(218^\circ\)[/tex]
The correct answer is [tex]\(62^\circ\)[/tex].
