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Answer :
The measure of angle BPC is 45 degrees.
To find the measure of angle BPC, let's follow these steps:
1. Understand the Problem: We're dealing with a regular octagon, where sides AB and CD are extended to meet at point P.
2. Identify Relevant Geometry: Recognize that when sides AB and CD are extended, they intersect at point P, forming angles such as angle APB and angle BPC.
3. Recognize Regular Octagon Properties: In a regular octagon, all interior angles are congruent, each measuring 135 degrees.
4. Analyze Vertical Angles: When AB and CD are extended and intersect at P, the angles formed are vertical angles, meaning they are congruent.
5. Calculate Angle APB: Since angle APB is a vertical angle to angle BPC, it also measures 135 degrees.
6. Determine Angle BPC: Angle BPC is the supplement of angle APB. Therefore, it equals 180 degrees minus 135 degrees, which equals 45 degrees.
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