Exercise 18 Page 592

Let's analyze the given triangle.

We can see that the measures of the interior angles are (x+8)^(∘) and 4x^(∘). 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. 7x-16=(x+8)+4x We will now solve the above equation for x.

7x-16=x+8+4x

AddTerms

Add terms

7x-16=5x+8

SubEqn

LHS-5x=RHS-5x

2x-16=8

AddEqn

LHS+16=RHS+16

2x=24

DivEqn

.LHS /2.=.RHS /2.

x=12

Now we can substitute x= 12 in the expression 7x-16 to find the measure of the angle. 7( 12)-16=68^(∘) Therefore, the measure of the exterior angle is 68^(∘).