Question

∠e and ∠f are complementary. the measure of ∠e is 54° more than the measure of ∠f. find the measure of each angle. m∠f = °. m∠e = °.

Explanation:

Step1: Set up equations

Let $m\angle F=x$. Then $m\angle E=x + 54$. Since $\angle E$ and $\angle F$ are complementary, $m\angle E+m\angle F = 90$. So, $(x + 54)+x=90$.

Step2: Simplify the equation

Combining like - terms, we get $2x+54 = 90$.

Step3: Solve for $x$

Subtract 54 from both sides: $2x=90 - 54$, so $2x=36$. Then divide both sides by 2: $x=\frac{36}{2}=18$.

Step4: Find the measure of $\angle E$

Since $m\angle E=x + 54$ and $x = 18$, then $m\angle E=18+54 = 72$.

Answer:

$m\angle F = 18$
$m\angle E = 72$