In triangle ABC, AB = AC. The measure of angle A is (2x)^, and the measure of angle B is (x + 15)^. What is the measure, in degrees, of angle C?

SAT Lines, angles, and triangles Practice Question 5 (Medium)

Question bank / Lines, angles, and triangles

Math · Geometry and TrigonometryMedium

In triangle $ABC$ , $AB = AC$ . The measure of angle $A$ is $(2x)^\circ$ , and the measure of angle $B$ is $(x + 15)^\circ$ . What is the measure, in degrees, of angle $C$ ?

$37.5$

$52.5$

$75$

$105$

Show answer and explanation

Answer: B

Since $AB = AC$ , the angles opposite those sides, $C$ and $B$ , are congruent, so angle $C$ also measures $(x + 15)^\circ$ . The angle sum gives $2x + 2(x + 15) = 180$ , so $4x = 150$ and $x = 37.5$ . Angle $C$ measures $37.5 + 15 = 52.5$ degrees.

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

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