In the figure above, and intersect at point P , , and . What is the measure, in degrees, of

Question

In the figure above, and intersect at point P , , and . What is the measure, in degrees, of ? (Disregard the degree symbol when gridding your answer.)

Accepted Answer

The correct answer is 30. It is given that the measure of is . Angle MPR and are collinear and therefore are supplementary angles. This means that the sum of the two angle measures is , and so the measure of is . The sum of the angles in a triangle is . Subtracting the measure of from yields the sum of the other angles in the triangle MPR. Since , the sum of the measures of and is . It is given that , so it follows that triangle MPR is isosceles. Therefore and must be congruent. Since the sum of the measure of these two angles is , it follows that the measure of each angle is . An alternate approach would be to use the exterior angle theorem, noting that the measure of is equal to the sum of the measures of and . Since both angles are equal, each of them has a measure of .

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