Exercise 12 Page 592

Let's analyze the given triangle.

We can see that the interior angles are 40^(∘) and 30^(∘). 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. 40+30+m∠ 1=180 By solving this equation, we will find the measure of ∠ 1.

40+30+m∠ 1=180

AddTerms

Add terms

70+m∠ 1=180

SubEqn

LHS-70=RHS-70

m∠ 1=110

The measure of ∠ 1 is 110^(∘). 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

Since we found that m∠ 1 equals 110^(∘), the triangle has an obtuse angle. Therefore, we can classify the triangle as obtuse.