The sum of the unknown angles is equal to m∠DEF.
m∠DEH=51^(∘)
m∠FEH=39^(∘)
Practice makes perfect
The expression m∠DEH indicates the measure of the angle between two rays, ED and EH. Similarly, the expression m∠FEH indicates the measure of the angle between rays EF and EH. To find their measures, let's start by identifying the three angles on a diagram.
Looking at the figures, and by the Angle Addition Postulate, we can see that m∠DEF is equal to the sum of m∠DEH and m∠FEH. We can solve for x by creating an equation using the expressions for the two smaller angles and the value of the larger angle. Note that ∠DEF is a right angle which is always equal to 90^(∘).
Having solved the equation, we can calculate the individual angles by substituting x= 3 into the expressions for the unknown angles.
m∠DEH:& 10( 3)+21=51^(∘)
m∠FEH:& 13( 3) =39^(∘)
