The sum of the unknown angles is equal to m∠EFG.
m∠EFH=70^(∘)
m∠HFG=30^(∘)
Practice makes perfect
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.
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^(∘)
