Points A, B, and C lie on a line, with B between A and C. Point D does not lie on the line. The measure of angle ABD is (3x)^, and the measure of angle DBC is (2x)^. What is the measure of angle ABD?

SAT Lines, angles, and triangles Practice Question 8 (Easy)

Question bank / Lines, angles, and triangles

Math · Geometry and TrigonometryEasy

Points $A$ , $B$ , and $C$ lie on a line, with $B$ between $A$ and $C$ . Point $D$ does not lie on the line. The measure of angle $ABD$ is $(3x)^\circ$ , and the measure of angle $DBC$ is $(2x)^\circ$ . What is the measure of angle $ABD$ ?

$36^\circ$

$72^\circ$

$108^\circ$

$144^\circ$

Show answer and explanation

Answer: C

Angles $ABD$ and $DBC$ form a linear pair, so their measures sum to $180^\circ$ : $3x + 2x = 180$ . So $x = 36$ , and angle $ABD$ measures $3(36) = 108^\circ$ .

Choice A is the value of $x$ , not the measure of angle $ABD$ .

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