Three distinct lines intersect at a single point, forming six... | SAT Lines, angles, and triangles Question, Answer Explained

Question bank / Lines, angles, and triangles

Math · Geometry and TrigonometryMedium

Three distinct lines intersect at a single point, forming six angles around the point that don't overlap. Two of these angles are adjacent and measure $40^\circ$ and $75^\circ$ . What is the measure of the other angle that is adjacent to the $75^\circ$ angle?

$40^\circ$

$65^\circ$

$105^\circ$

$140^\circ$

Show answer and explanation

Answer: B

Each line forms a straight angle, $180^\circ$ , through the point. With three lines, each straight angle is split into three adjacent angles. The $40^\circ$ angle, the $75^\circ$ angle, and the next angle around the point together form a straight angle, so the next angle measures $180^\circ - 40^\circ - 75^\circ = 65^\circ$ .

Choice C assumes the $75^\circ$ angle and its neighbor form a linear pair, but with three lines, each straight angle is split into three angles, not two.

Why the other choices are wrong

A. The 40 degree angle is the neighbor on one side. The neighbor on the other side completes a straight angle with the 40 and 75 degree angles.
C. With three lines, a straight angle is split into three angles, not two, so 75 and its neighbor don't form a linear pair.
D. 140 degrees is 180 minus 40, which ignores the 75 degree angle.

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