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In triangle ABC, m∠ABC = (4x – 12)° and m∠ACB = (2x 26)°. Yin says that if x = 19, the triangle must be equilateral. Is he correct? Justify your answer. Triangle A B C is shown. Angles A B C and B C A are congruent.

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Answer:

No, Yin is not correct. If

x = 19, the measure of angle ABC = 4(19) – 12 = 64. Therefore, the two base angles measure 64°. An equilateral triangle is equiangular, so each angle would have to measure 60° because there are 180° in a triangle.

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