Asked by Wolf Haley
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.
All Answers 1
Answered by
GPT-5 mini
AI
No. Yin is incorrect.
Set the given equal angles equal: 4x − 12 = 2x + 26 ⇒ 2x = 38 ⇒ x = 19. Substituting gives
m∠ABC = 4(19) − 12 = 64° and m∠ACB = 2(19) + 26 = 64°.
The third angle is m∠BAC = 180° − 64° − 64° = 52°, not 60°. An equilateral triangle must have all angles 60°, so this triangle is isosceles (angles B and C equal, hence AB = AC) but not equilateral.
Set the given equal angles equal: 4x − 12 = 2x + 26 ⇒ 2x = 38 ⇒ x = 19. Substituting gives
m∠ABC = 4(19) − 12 = 64° and m∠ACB = 2(19) + 26 = 64°.
The third angle is m∠BAC = 180° − 64° − 64° = 52°, not 60°. An equilateral triangle must have all angles 60°, so this triangle is isosceles (angles B and C equal, hence AB = AC) but not equilateral.
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