Exercise 3 Page 591

Consider the given diagram of a triangle.

We want to find the measure of ∠ 1. To do so, recall that 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. Let's write an equation applying this theorem. 5x-10=40+3xWe will now solve the above equation for x.

5x-10=40+3x

AddEqn

LHS+10=RHS+10

5x=50+3x

SubEqn

LHS-3x=RHS-3x

2x=50

DivEqn

.LHS /2.=.RHS /2.

x=25

Now we can substitute x= 25 into the expression 3x to find the measure of this angle. 3( 25)=75 The Triangle Angle-Sum Theorem states that the measures of the interior angles of a triangle add up to 180. Therefore, knowing that the measures of two of the interior angles are 40 and 75, we can write an equation to find m∠ 1. 40+75+ m∠ 1=180 We can find the measure of ∠ 1 by solving this equation. Let's do it!

40+75+m∠ 1=180

AddTerms

Add terms

115+m∠ 1=180

SubEqn

LHS-115=RHS-115

m∠ 1=65

Therefore, the measure of ∠ 1 is 65^(∘).