To determine the measure of arc AB given that the measure of angle APB is 78 degrees, we first need to understand the relationship between an inscribed angle and the arc it subtends in a circle.
When an angle is inscribed in a circle, the measure of the angle is always half the measure of the intercepted arc. In this case, angle APB is inscribed and intercepts arc AB.
Thus, the formula we can use is:
- Measure of arc AB = 2 * Measure of angle APB
Plugging in the values, we get:
- Measure of arc AB = 2 * 78 degrees
- Measure of arc AB = 156 degrees
Therefore, the measure of arc AB is 156 degrees.
In summary, when the measure of angle APB is 78 degrees, the corresponding measure of arc AB is calculated to be 156 degrees, following the fundamental principle of inscribed angles.