Two lines intersect at a point, forming two pairs of vertical angles. One angle measures (3x + 10)^, and the angle vertical to it measures (5x - 30)^. What is the value of x?

SAT Lines, angles, and triangles Practice Question 4 (Medium)

Question bank / Lines, angles, and triangles

Math · Geometry and TrigonometryMedium

Two lines intersect at a point, forming two pairs of vertical angles. One angle measures $(3x + 10)^\circ$ , and the angle vertical to it measures $(5x - 30)^\circ$ . What is the value of $x$ ?

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Answer: 20

Vertical angles are congruent, so $3x + 10 = 5x - 30$ . Subtracting $3x$ and adding $30$ to both sides gives $40 = 2x$ , so $x = 20$ . (Each angle measures $70^\circ$ .)

Setting the expressions to sum to $180$ gives $x = 25$ , which would be correct for adjacent angles, not vertical angles.

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