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 \(m\angle R=x\). Then \(m\angle Q = x - 26\). Since \(\angle Q\) and \(\angle R\) are complementary, \(m\angle Q+m\angle R = 90\). Substitute the expressions: \((x - 26)+x=90\).

Step2: Solve the equation

Combine like - terms: \(2x-26 = 90\). Add 26 to both sides: \(2x=90 + 26\), so \(2x=116\). Divide both sides by 2: \(x=\frac{116}{2}=58\).

Step3: Find \(m\angle Q\)

Substitute \(x = 58\) into \(m\angle Q=x - 26\). Then \(m\angle Q=58-26 = 32\).

Answer:

\(m\angle Q = 32\)
\(m\angle R = 58\)