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Given: ABCD is a straight line. Angle PBQ and PCQ are right angles. Angle X = Angle Y. Prove: Angle ABQ = Angle DCQ.

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Final answer:

To prove that Angle ABQ is equal to Angle DCQ, we can make use of the given information and apply the properties of a straight line and right angles.

Step-by-step explanation:

To prove that Angle ABQ is equal to Angle DCQ, we can make use of the given information and apply the properties of a straight line and right angles. Since ABCD is a straight line, Angle ABQ + Angle PBQ = 180 degrees and Angle DCQ + Angle PCQ = 180 degrees. It is also given that Angle X = Angle Y. Therefore, Angle ABQ + Angle PBQ = Angle DCQ + Angle PCQ.

Since Angle PBQ and Angle PCQ are right angles, we know that Angle PBQ + Angle PCQ = 90 degrees. Substitute this value into the previous equation and we get Angle ABQ + 90 degrees = Angle DCQ + 90 degrees. Since 90 degrees is the same for both equations, we can subtract 90 degrees from both sides to get Angle ABQ = Angle DCQ. Hence, we have proven that Angle ABQ is equal to Angle DCQ.

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