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

Sample Response: 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.

What did you include in your response? Check all that apply.

Yin is not correct.

The measure of the congruent base angles is 64°.

The measures of the angles in an equilateral triangle are 60°.

Answer 2

A triangle is equilateral if all three angles are same. but here two angles are 64° but third angle is 52°. so, Yin is incorrect.

Explanation:

x = 19,

Putting value of x to find m∠ABC and m∠ACB

m∠ABC = (4x – 12)°

m∠ABC = (4(19) – 12)°

m∠ABC = (76 – 12)°

m∠ABC = 64°

m∠ACB = (2(19) + 26)°

m∠ACB = (38 + 26)°

m∠ACB = 64°

now we know sum of angles of triangle is 180°. We can find the measure of third angle.

180 = 64+64 +x

x= 180 - 64 - 64

x = 52°

A triangle is equilateral if all three angles are same. but here two angles are 64° but third angle is 52°. so, Yin is incorrect.