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GRE
GRE Quantitative Reasoning Section

Finding Vertical Angles in Intersecting Lines

Medium Geometry Lines And Angles

In a geometric configuration, two lines intersect at point P, creating four angles: $ heta_1$, $ heta_2$, $ heta_3$, and $ heta_4$. The measures of these angles are related as follows:

If $ heta_1 = 2 heta_2$ and $ heta_3 = heta_2 + 30^{ ext{°}}$, what is the measure of $ heta_1$?

Note that angles $ heta_1$ and $ heta_3$ are vertical angles, and angles $ heta_2$ and $ heta_4$ are also vertical angles. Remember that vertical angles are equal, and the sum of the angles around point P (all four angles) must equal $360^{ ext{°}}$.

Hint

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