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Big Ideas Math Integrated I, 2016

BI

Big Ideas Math Integrated I, 2016 View details

1. Angles of Triangles

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Exercise 11 Page 592

Consider the Triangle Angle-Sum Theorem.

m∠ 1=71^(∘)
Triangle: Acute

Practice makes perfect

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

Add terms

109+m∠ 1=180

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.

Subchapter links

Communicate Your Answer p.587

Monitoring Progress p.588-591

Exercises p.592-594