Exercise 7 Page 149

Practice makes perfect

a Let's look at the given diagram to identify angles d and k.

These are alternate interior angles. The Alternate Interior Angles Theorem tells us that alternate interior angles formed by parallel lines and a transversal are congruent, so we know that the measures of ∠ d and ∠ k are equal. m ∠ d &= m ∠ k &⇓ 110^(∘) &= 5x-20^(∘) Let's solve the equation for x.

110^(∘) = 5x - 20^(∘)

AddEqn

LHS+20^(∘)=RHS+20^(∘)

130^(∘) = 5x

DivEqn

.LHS /5.=.RHS /5.

26^(∘) = x

RearrangeEqn

Rearrange equation

x = 26^(∘)

b Let's look at the given diagram to identify angles b and n.

These are consecutive exterior angles. The Consecutive Exterior Angles Theorem tells us that consecutive exterior angles formed by parallel lines and a transversal are supplementary — the sum of the measures of these angles will be 180 ^(∘). m ∠ b &+ m ∠ n = 180^(∘) & ⇓ (4x-11^(∘)) &+ (x+26^(∘)) = 180^(∘) Let's solve the equation for x.

(4x-11^(∘)) + (x+26^(∘)) = 180^(∘)

▼

Solve for x

RemovePar

Remove parentheses

4x-11^(∘)+x+26^(∘) = 180^(∘)

AddTerms

Add terms

5x+15^(∘) = 180^(∘)

SubEqn

LHS-15^(∘)=RHS-15^(∘)

5x = 165^(∘)