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GRE
GRE Quantitative Reasoning Section

Finding the Angle Measures of Intersecting Lines

Very Hard Geometry Lines And Angles

In the accompanying diagram, two lines intersect at point O, creating four angles: ∠AOB, ∠BOC, ∠COD, and ∠DOA. If the measure of angle ∠AOB is given as $x$ degrees, and it is known that the measure of angle ∠COD is twice that of ∠AOB, what is the measure of the angle ∠DOA?

Also, if the sum of angle ∠BOC and angle ∠DOA is equal to $180^{ ext{o}}$, what is the value of $x$?

Assume that all angles are measured in degrees.

Hint

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