Exercise 16 Page 41

Practice makes perfect

a We have been asked to find the value of x. The expression m∠ ABC is the angle measure between the rays BA and BC. Similarly, m∠ CBD is the angle measure between the rays BC and BD.

The sum of m∠ ABC and m∠ CBD is equal to m∠ ABD. m∠ ABC+ m∠ CBD= m∠ ABD Let's substitute given expressions for the two smaller angles into the equation. Then we can solve for x.

m∠ ABC+ m∠ CBD= m∠ ABD

SubstituteExpressions

Substitute expressions

( 2x)+( 3x)= 180

▼

Solve for x

RemovePar

Remove parentheses

2x+3x=180

AddTerms

Add terms

5x=180

DivEqn

.LHS /5.=.RHS /5.

x=36

b Having solved the equation, we can calculate the individual angles by substituting x= 36 into the expressions for the unknown angles.

m∠ ABC &: 2( 36)^(∘)=72^(∘) m∠ CBD &: 3( 36)^(∘)=108^(∘) Now, we can classify the angles using their measure.

Type	Measure
Acute	0^(∘)
Right	m=90^(∘)
Obtuse	90^(∘)
Straight	m=180^(∘)

We know that m∠ ABC = 72^(∘), so this angle is acute. On the other hand, m∠ CBD = 108^(∘), so ∠ CBD is obtuse.

Exercise 16 Page 41

Hints

Check the answer

Practice exercises

Asses your skill