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

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.

Answer 2

If x = 19   m∠ABC = (4.19 – 12)°=64°, and m∠ACB = (2.19 + 26)°=64°
so the other angle can be found with
m∠ABC + m∠ACB + m∠CAB =180°
 m∠CAB =180°-m∠ABC -m∠ACB =180°-128°=52°
so the triangle is not aquilateral, 
he was wrong