Exercise 6 Page 392

We want to find the measure of ∠ KJP 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 ∠ LJK. m ∠ LJK = 6( 5)^(∘) = 30^(∘) Let's add this value to out diagram.

Finally, let's notice ∠ KJP and ∠ LJK are a pair of adjacent angles making a straight line. Therefore, these angles are supplementary and the sum of their measures equals 180^(∘). Since we know the measure of ∠ LJK, let's use it to write an equation for m ∠ KJP and solve it. m ∠ KJP + 30^(∘) = 180^(∘) ⇒ m ∠ KJP = 150^(∘)