In triangle ABC, the exterior angle at vertex C measures 130^. The measure of angle A is 20^ greater than the measure of angle B. What is the measure, in degrees, of angle A?

SAT Lines, angles, and triangles Practice Question 15 (Medium)

Question bank / Lines, angles, and triangles

Math · Geometry and TrigonometryMedium

In triangle $ABC$ , the exterior angle at vertex $C$ measures $130^\circ$ . The measure of angle $A$ is $20^\circ$ greater than the measure of angle $B$ . What is the measure, in degrees, of angle $A$ ?

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Answer: 75

An exterior angle of a triangle equals the sum of the two remote interior angles, so $m\angle A + m\angle B = 130$ . With $m\angle A = m\angle B + 20$ , we get $2m\angle B + 20 = 130$ , so $m\angle B = 55$ and $m\angle A = 75$ .

Answering $55$ gives the measure of angle $B$ , not angle $A$ .

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