Question

Triangle ABC is inscribed in a circle. The measure of angle B is 88 degrees and angle C is 41 degrees. If point P is the midpoint of arc AB, what is angle PAC?

Answer 1

The measure of angle PAC is half of the measure of arc APB, which can be found by subtracting the given angles in the triangle from 180 degrees.

Step-by-step explanation:

Triangle ABC is inscribed in a circle with point P as the midpoint of arc AB. Since point P is the midpoint of the arc, the measure of angle PAC is equal to half of the measure of arc APB. To find the measure of arc APB, we can use the fact that the sum of the angles in a triangle is 180 degrees. Therefore, angle APB is equal to 180 - angle B - angle C. Plugging in the given values of 88 degrees for angle B and 41 degrees for angle C, we find that angle APB is 180 - 88 - 41 = 51 degrees. Finally, since angle PAC is half of angle APB, angle PAC is 51/2 = 25.5 degrees.