Question

∠q and ∠r are complementary. the measure of ∠q is 26° less than the measure of ∠r. find the measure of each angle. m∠q = m∠r =

Explanation:

Step1: Set up equations

Let $m\angle Q = x$ and $m\angle R=y$. Since $\angle Q$ and $\angle R$ are complementary, $x + y=90$. Also, $x=y - 26$.

Step2: Substitute equation

Substitute $x=y - 26$ into $x + y=90$. We get $(y - 26)+y=90$.

Step3: Simplify the equation

Combine like - terms: $2y-26 = 90$. Add 26 to both sides: $2y=90 + 26=116$.

Step4: Solve for $y$

Divide both sides of $2y = 116$ by 2: $y=\frac{116}{2}=58$.

Step5: Solve for $x$

Substitute $y = 58$ into $x=y - 26$. Then $x=58 - 26 = 32$.

Answer:

$m\angle Q = 32^{\circ}$
$m\angle R = 58^{\circ}$