Exercise 32 Page 395

Let's consider the given diagram.

We see that we have three adjacent angles that sum to the straight angle ∠ JGF. Therefore, the sum of their measures equals the measure of ∠ JGF — 180^(∘). Let's write this fact as an equation for x. Also, note that the measure of ∠ KGL is 90^(∘). x^(∘)+ 90^(∘) + 8x^(∘) = 180^(∘) Let's solve the above equation!

x^(∘)+90^(∘) + 8x^(∘) = 180^(∘)

AddTerms

Add terms

9x^(∘) + 90^(∘) = 180^(∘)

SubEqn

LHS-90^(∘)=RHS-90^(∘)

9x^(∘) = 90^(∘)

DivEqn

.LHS /9.=.RHS /9.

x^(∘) = 10^(∘)

We found that x^(∘) = 10^(∘). Now, we will substitute x^(∘)=10^(∘) into the angle 8x^(∘) to find its exact value.

8x^(∘)

Substitute

x= 10

8( 10)^(∘)

Multiply

Multiply

80 ^(∘)

Finally, let's list the found angle measurements. ∠ FGL=10^(∘) and ∠ KGJ=80 ^(∘)