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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 17 Page 592

Consider the Exterior Angle Theorem.

114^(∘)

Practice makes perfect

Let's analyze the given triangle.

We can see that the interior angles angles are 24^(∘) and (2x+18)^(∘). According to the Exterior Angle Theorem, the measure of an exterior angle of a triangle is equal to the sum of the measures of the two nonadjacent interior angles. This allows us to write an equation. 3x+6=24+(2x+18) We will now solve the above equation for x.

3x+6=24+2x+18

Add terms

3x+6=42+2x

LHS-2x=RHS-2x

x+6=42

LHS-6=RHS-6

x=36

Now we can substitute x= 36 in the expression 3x+6 to find the measure of the angle. 3( 36)+6=114^(∘) Therefeore, the measure of the exterior angle is 114^(∘).

Subchapter links

Communicate Your Answer p.587

Monitoring Progress p.588-591

Exercises p.592-594