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 cor

Question

BabaBlast [244]

2 years ago

10

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 cor

rect? Justify your answer

Mathematics

2 answers:

spin [16.1K] · Answer 1 · 2022-07-24T21:16:01+03:00

He is not correct. If this is to be an equilateral triangle then all the angles must be the same measure. That means that 180/3 = 60°. They all have to equal 60°. If one of the angles measures 4x-12, then 4x-12=60. Solving for x, we will add 12 to both sides to get 4x=72. x here is 18. For the other angle measuring 2x+26, we would do the same. 2x+26=60. Subtract 26 from both sides to get 2x= 34 and x = 17. He was way off.

andreyandreev [35.5K] · Answer 2 · 2022-07-24T23:28:13+03:00

andreyandreev [35.5K]2 years ago

4 0

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 quadrangular, so each angle would have to measure 60° because there are 180° in a triangle.