Exercise 14 Page 592

Let's analyze the given triangle.

We can see that both interior angles are 60^(∘). According to the Triangle Angle-Sum Theorem the measures of the interior angles of a triangle add to 180^(∘). Let's write this as an equation. 60+60+m∠ 1=180 By solving this equation, we will find the measure of ∠ 1.

60+60+m∠ 1=180

AddTerms

Add terms

120+m∠ 1=180

SubEqn

LHS-120=RHS-120

m∠ 1=60

The measure of ∠ 1 is also 60^(∘). Now, we can classify the triangle by its angles.

Type	Angles
Acute	3 acute angles
Right	1 right angle
Obtuse	1 obtuse angle
Equiangular	3 congruent angles

In our case, since all the angles are equal 60^(∘), they are congruent. Therefore, we know that the triangle is equiangular.