Exercise 5 Page 392

We want to find the measure of ∠ NJM using the following diagram.

First, let's find the value of x. We notice that ∠ LJK and ∠ PJN are vertical angles, so they have the same measure.

Now, ∠ PJN and ∠ NJM are complementary angles — the sum of their measures equals 90^(∘). Let's write this fact as an equation for x and solve it!

6x^(∘)+ 12^(∘)=90^(∘)

AddTerms

Add terms

18x^(∘) = 90^(∘)

DivEqn

.LHS /18.=.RHS /18.

x^(∘) = 5^(∘)

Now that we know the value of x, let's substitute it into the expression for the measure of ∠ NJM. m ∠ NJM = 12( 5)^(∘) = 60^(∘)