The measure of angle Q equals the measure of angle O. Angle O is larger than angle Q. The correct option is D.
What is triangle?
Triangle is a shape made of three sides in a two-dimensional plane. the sum of the three angles is 180 degrees.
Consider attached diagram, where MQ = QP = PO = ON. Check all the options one by one.
Option A is false because segment OP is equal to segment MQ (given).
Option B is false because segment MN has a length that depends on the placement of points M and N (segment MN can be greater than segment MP, can be smaller than segment MP).
Option C is false, because if the measure of angle Q equals the measure of angle O, then by the cosine law, MP=NP but this statement is not true (given MP<NP).
Option D is true because the side that is opposite to the greater angle is greater and you know that MN>NP, then the measure of angle O is larger than the measure of the angle Q.
Therefore, the measure of angle Q equals the measure of angle O. Angle O is larger than angle Q. The correct option is D.
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