Question

∠a and ∠b are complementary. the measure of ∠a is 16° more than the measure of ∠b. find the measure of each angle. m∠b = m∠a = need help with this question? get a hint show answer

Explanation:

Step1: Define variables

Let the measure of $\angle F=x$. Then the measure of $\angle K = x + 54^{\circ}$.

Step2: Use the complementary - angle property

Since $\angle K$ and $\angle F$ are complementary, $\angle K+\angle F = 90^{\circ}$. Substitute the expressions for the angles: $(x + 54^{\circ})+x=90^{\circ}$.

Step3: Simplify the equation

Combine like - terms: $2x+54^{\circ}=90^{\circ}$. Then subtract $54^{\circ}$ from both sides: $2x=90^{\circ}-54^{\circ}=36^{\circ}$.

Step4: Solve for $x$

Divide both sides of the equation $2x = 36^{\circ}$ by 2: $x=\frac{36^{\circ}}{2}=18^{\circ}$.

Step5: Find the measure of $\angle K$

Substitute $x = 18^{\circ}$ into the expression for $\angle K$: $\angle K=x + 54^{\circ}=18^{\circ}+54^{\circ}=72^{\circ}$.

Answer:

$m\angle F = 18^{\circ}$
$m\angle K = 72^{\circ}$