Exercise 9 Page 41

We have been asked to find the measures of ∠ EFH and ∠ HFG.

Because ∠ EFH and ∠ HFG are adjacent angles, the Angle Addition Postulate tells us that the sum of m∠ EFH and m∠ HFG is equal to m∠ EFG. m∠ EFH+ m∠ HFG= m∠ EFG We are also told that ∠ EFG is a right angle so its measure is 90 ^(∘). Let's substitute this, and the given expressions into the equation. Then we can solve for x.

m∠ EFH+m∠ HFG=m∠ EFG

SubstituteValues

Substitute values

( 2x+2)+( x+1)= 90

RemovePar

Remove parentheses

2x+2+x+1=90

AddTerms

Add terms

3x+3=90

SubEqn

LHS-3=RHS-3

3x=87

DivEqn

.LHS /3.=.RHS /3.

x=29

Having solved the equation, we can calculate the individual angles by substituting x= 29 into the expressions for the unknown angles. m∠ EFH:& 2( 29)+2=70^(∘) m∠ HFG:& 29+1 =30^(∘)