Exercise 11 Page 592

Let's analyze the given triangle.

We can see that the interior angles are 78^(∘) and 31^(∘). According to the Triangle Angle-Sum Theorem, the measures of the interior angles of a triangle add to 180^(∘). This allows us to write an equation. 78+31+m∠ 1=180 By solving this equation, we will find the measure of ∠ 1.

78+31+m∠ 1=180

AddTerms

Add terms

109+m∠ 1=180

SubEqn

LHS-109=RHS-109

m∠ 1=71

The measure of ∠ 1 is 71^(∘). 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 acute, we know that the triangle is acute.