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GRE
GRE Quantitative Reasoning Section

Comparison of Sums of Angles in a Right Triangle

Hard Geometry Lines And Angles

In a right triangle, each of the legs is extended to form two angles with the original legs. Let the right triangle be triangle ABC, where angle B is the right angle. The leg BC measures 6 units and leg AB measures 8 units.

When extending leg BC, an angle of $x^ heta$ degrees is formed with leg AC, and when extending leg AB, an angle of $y^ heta$ degrees is formed with leg AC. If we know that angle C is equal to angle y and that angle A is equal to angle x, what is the relationship between the sum of angles y and x?

Provide your answer based on the following quantities:

Quantity A: The sum of angles $x$ and $y$.

Quantity B: 90 degrees.

Hint

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