In triangle ABC, angle A = 80 degrees. The bisector of angle B and angel C intersect at point P. Angle BPC = what?

angle BPC=180-1/2 (B+C)

but B+C=180-A

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100

110

To find the measure of angle BPC, we can use the property of angle bisectors.

First, let's understand what the concept of an angle bisector means. An angle bisector is a line or ray that splits an angle into two equal angles. In triangle ABC, the bisector of angle B and angle C intersects at point P. This means that angle ABP is equal to angle CBP and angle ACP is equal to angle BCP.

Now, let's consider the angles in triangle BPC. Angle BPC is composed of two angles: angle ABP and angle ACP. Since the angle bisectors divide their respective angles into two equal parts, angle ABP and angle ACP are both equal to half of their respective angles.

Given that angle A is 80 degrees, we know that angle ABP and angle ACP are both equal to 80/2 = 40 degrees.

Therefore, angle BPC is equal to angle ABP + angle ACP, which is 40 degrees + 40 degrees = 80 degrees.

Hence, the measure of angle BPC in triangle ABC is 80 degrees.