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

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.

Yin is incorrect because when the value of x is 19 both the angles is equal to but in equilateral triangle all the angles must be equal to and this can be determine by using the properties of equilateral triangle.

Given :

In triangle ABC, ABC = (4x – 12)° and ACB = (2x + 26)°.

In equilateral triangle all the three sides of the triangle are equal and all the interior angles are congruent to each other and equal to .

So, to prove that the given triangle ABC is an equilateral triangle than both the given angles must be equal to .

= 76 - 12

=

= 38 + 26

=

Therefore, Yin is incorrect because when the value of x is 19 both the angles is equal to but in equilateral triangle all the angles must be equal to .

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