Question

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

Answer 1

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.

Answer 2

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.