In triangle ABC, AB = BC, and the measure of angle B is 40^. What is the measure of angle A?

In triangle ABC, AB = BC, and the measure of angle B is 40^... | SAT Lines, angles, and triangles Question, Answer Explained

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In triangle $ABC$ , $AB = BC$ , and the measure of angle $B$ is $40^\circ$ . What is the measure of angle $A$ ?

$40^\circ$

$70^\circ$

$100^\circ$

$140^\circ$

Show answer and explanation

Answer: B

Because $AB = BC$ , the angles opposite these sides are congruent. Angle $C$ is opposite $\overline{AB}$ and angle $A$ is opposite $\overline{BC}$ , so angles $A$ and $C$ have equal measures. The angles of a triangle sum to $180^\circ$ , so $2(m\angle A) + 40^\circ = 180^\circ$ , which gives $m\angle A = 70^\circ$ .

Choice A assumes that angle $A$ is congruent to angle $B$ , but the congruent angles are the ones opposite the equal sides, angles $A$ and $C$ .

Why the other choices are wrong

A. The congruent angles are opposite the equal sides, so angle A matches angle C, not angle B.
C. This would be angle C if angles A and B were both 40 degrees, but they aren't congruent.
D. 140 degrees is the sum of angles A and C together.

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