Exercise 22 Page 340

Practice makes perfect

We will begin by writing an equation to find x. Then, we will find the measure of ∠ JKL.

Notice that we are given the measure of an exterior angle of △ JKL. We are also given expressions for two remote interior angles at J and K.

In this case, let's recall the Triangle Exterior Angle Theorem.

Triangle Exterior Angle Theorem
The measure of the exterior angle is the sum of the measures of the two remote interior angles.

By this theorem, we can write an equation and solve it for x.

m∠ J+m∠ K=100

m∠ J= 2x+27, m∠ K= 2x-11

2x+27+ 2x-11=100

▼

Solve for x

Add and subtract terms

4x+16=100

LHS-16=RHS-16

4x=84

.LHS /4.=.RHS /4.

x=21

The value of x on the diagram is 21.

Since we found the value of x, we can now find the measure of ∠ JKL by substituting x= 21 into the expression of m∠ JKL.

m∠ JKL=2x-11

x= 21

m∠ JKL=2( 21)-11

m∠ JKL=42-11

Subtract term

m∠ JKL=31

The measure of ∠ JKL is 31^(∘).

Exercises p.339-343

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