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Answer :
Final answer:
To find the measure of angle BPC, we need to use the property of angles in a circle. Since M is the midpoint of arc AB, angle BMA is equal to half the measure of arc AB. Similarly, since N is the midpoint of arc BC, angle BNC is equal to half the measure of arc BC.
Explanation:
To find the measure of angle BPC, we need to use the property of angles in a circle.
Since M is the midpoint of arc AB, angle BMA is equal to half the measure of arc AB. Similarly, since N is the midpoint of arc BC, angle BNC is equal to half the measure of arc BC.
Since a circle has a total of 360 degrees, we can find the measure of arc AB and arc BC by doubling the given angles.
Therefore, arc AB = 2 * 12° = 24° and arc BC = 2 * 12° = 24°.
Since arc AB and arc BC together make up the entire circle, the measure of angle BPC is equal to the sum of the measures of arcs AB and arc BC.
Therefore, angle BPC = arc AB + arc BC = 24° + 24° = 48°.
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