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Problem 581

To construct an angle whose measure is equal to the sum of the measures of two given angles.

Expert verified

To construct an angle whose measure is equal to the sum of the measures of two given angles, follow these steps: 1) Construct the two given angles separately using a compass and straightedge. 2) Calculate the sum of their measures. 3) Use the compass and straightedge to construct the final angle, using the sum of the measures as the angle's measure. This involves drawing a straight line segment as the initial side, placing the compass on the vertex and drawing an arc, measuring the sum using a protractor, and marking the final angle's measure on the arc. Finally, draw a straight line segment from the vertex to the point marked on the arc as the terminal side of the angle.

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