Question

∠q and ∠r are complementary. the measure of ∠q is 28° less than the measure of ∠r. find the measure of each angle.

m∠q =

m∠r =

Explanation:

Step1: Define variables

Let \(m\angle R=x\). Then \(m\angle Q = x - 28\).

Step2: Use complementary - angle property

Since \(\angle Q\) and \(\angle R\) are complementary, \(m\angle Q+m\angle R = 90\).
Substitute the expressions for \(m\angle Q\) and \(m\angle R\): \((x - 28)+x=90\).

Step3: Solve the equation

Combine like terms: \(2x-28 = 90\).
Add \(28\) to both sides: \(2x=90 + 28=118\).
Divide both sides by \(2\): \(x=\frac{118}{2}=59\).

Step4: Find \(m\angle Q\)

Substitute \(x = 59\) into \(m\angle Q=x - 28\). Then \(m\angle Q=59-28 = 31\).

Answer:

\(m\angle Q = 31^{\circ}\), \(m\angle R=59^{\circ}\)