Question

1. ∠q and ∠r are complementary. the measure of ∠q is 26° less than the measure of the angle. find the measure of each angle.
2. the measure of the supplement of an angle is three times the measure of the angle. find the measures of the angle and its supplement.

Explanation:

Step1: Define variables for problem 4

Let the measure of $\angle R=x$. Then the measure of $\angle Q = x - 26$. Since $\angle Q$ and $\angle R$ are complementary, $\angle Q+\angle R = 90^{\circ}$.
So, $(x - 26)+x=90$.

Step2: Solve the equation for problem 4

Combine like - terms: $2x-26 = 90$.
Add 26 to both sides: $2x=90 + 26=116$.
Divide both sides by 2: $x=\frac{116}{2}=58$.
So, $\angle R = 58^{\circ}$ and $\angle Q=58 - 26 = 32^{\circ}$.

Step3: Define variable for problem 5

Let the measure of the angle be $y$. Its supplement is $180 - y$.
We are given that $180 - y=3y$.

Step4: Solve the equation for problem 5

Add $y$ to both sides: $180=3y + y=4y$.
Divide both sides by 4: $y=\frac{180}{4}=45$.
The angle is $45^{\circ}$ and its supplement is $180 - 45=135^{\circ}$.

Answer:

For problem 4: $\angle Q = 32^{\circ}$, $\angle R = 58^{\circ}$.
For problem 5: The angle is $45^{\circ}$, its supplement is $135^{\circ}$.