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Geometry and Trigonometry Difficulty: Medium
The figure presents two triangles, triangle A, B C and triangle D E F. The two triangles are placed side by side, and triangle A, B C is larger than triangle D E F. In triangle A, B C, side A, B slants upward and to the right, side B C slants downward and to the right, and side A, C slants slightly upward and to the right. In triangle D E F, side D E slants upward and to the right, side E F slants downward and to the right, and side D F slants slightly upward and to the right. A note indicates that the figures are not drawn to scale.

Triangle ABC and triangle DEF are shown. The relationship between the side lengths of the two triangles is such that the length of side A, B, over, the length of side D E, equals, the length of side B C, over, the length of side E F, which equals, the length of side A, C, over, the length of side D F, which equals 3. If the measure of angle BAC is 20°, what is the measure, in degrees, of angle EDF ? (Disregard the degree symbol when gridding your answer.)

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Explanation

The correct answer is 20. By the equality given, the three pairs of corresponding sides of the two triangles are in the same proportion. By the side-side-side (SSS) similarity theorem, triangle ABC is similar to triangle DEF. In similar triangles, the measures of corresponding angles are congruent. Since angle BAC corresponds to angle EDF, these two angles are congruent and their measures are equal. It’s given that the measure of angle BAC is 20°, so the measure of angle EDF is also 20°.