SAT Lines, Angles & Triangles Question 38 | Free SAT Prep

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Question 38·Medium·Lines, Angles, and Triangles

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In $\triangle ABC$ , $\overline{AB}=\overline{AC}$ , and side $\overline{AC}$ is extended through $C$ to point $D$ . If the measure of exterior angle $\angle BCD$ is $132^\circ$ , what is $m\angle B$ ?

For an isosceles-triangle question with an extended side, first use the linear pair formed by the interior and exterior angles to find the interior angle at the extension point. Then use the fact that angles opposite equal sides have equal measures.

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Use the straight line at $C$

The interior angle at $C$ and exterior angle $\angle BCD$ form a linear pair, so their measures sum to $180^\circ$ .

Use the equal-side relationship

Determine which two angles are equal when $\overline{AB}=\overline{AC}$ .

Connect the results

After finding the interior angle at $C$ , use the equal base angles of the isosceles triangle to determine $m\angle B$ .

Desmos Guide

Calculate the supplementary angle

Enter 180-132 in Desmos to find the measure of the interior angle at $C$ . Then use $\overline{AB}=\overline{AC}$ to verify that $\angle B$ has the same measure.

Step-by-step Explanation

Find the interior angle at $C$

The interior angle $\angle ACB$ and exterior angle $\angle BCD$ form a straight line, so their measures add to $180^\circ$ :

m\angle ACB+132^\circ=180^\circ

Thus,

m\angle ACB=48^\circ

Use the equal sides

Since $\overline{AB}=\overline{AC}$ , the angles opposite those sides are equal. Therefore,

m\angle B=m\angle C

Because $m\angle C=48^\circ$ , it follows that

m\angle B=48^\circ

Thus, the correct choice is B.

Strategy

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Desmos Guide

Step-by-step Explanation

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Strategy

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Desmos Guide

Step-by-step Explanation