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Quadrilateral PQRS is an isosceles trapezoid in which mZP = m2. Which of the following statements must be true?

a) The sum of angles P and Q is 90 degrees.
b) The sum of angles P and Q is 180 degrees.
c) The sum of angles P and Q is 360 degrees.
d) The sum of angles P and Q cannot be determined based on the given information.

User Thr
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Final answer:

In an isosceles trapezoid, the sum of angles P and Q must be 180 degrees because they form a linear pair.

Step-by-step explanation:

The student is asking about the properties of an isosceles trapezoid, specifically regarding the relationship between two of its angles. An isosceles trapezoid is a four-sided figure with one pair of parallel sides and the other sides being of equal length. In an isosceles trapezoid, the angles adjacent to the base are equal, and the angles adjacent to the non-parallel sides (the other base) are also equal. Due to this, the sum of each pair of adjacent angles is 180 degrees because these angles form a linear pair. Therefore, the sum of angles P and Q in isosceles trapezoid PQRS must be 180 degrees.

It's important to note that this question revolves around geometry and the properties of specific geometric figures. As such, we used the concept of a linear pair of angles which occurs when two angles share a common side and their other sides form a line. This is why the sum of the angles P and Q is 180 degrees.

User Rich Seviora
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