Question

1. the measure of an angles supplement is 76° less than the measure of the angle. find the measures of the angle and its supplement.
2. ∠q and ∠r are complementary. the measure of ∠q is 26° less than the measure of ∠r. find the measure of each angle.
3. 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:

6.

Step1: Let the angle be $x$.

Its supplement is $180 - x$. Given that $180 - x=x - 76$.

Step2: Solve the equation for $x$.

Add $x$ to both sides: $180=2x - 76$. Then add 76 to both sides: $2x=180 + 76=256$. Divide both sides by 2: $x = 128^{\circ}$. The supplement is $180-128 = 52^{\circ}$.

Step1: Let the measure of $\angle R$ be $x$.

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

Step2: Solve the equation for $x$.

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

Step1: Let the angle be $x$.

Its supplement is $180 - x$. Given that $180 - x=3x$.

Step2: Solve the equation for $x$.

Add $x$ to both sides: $180 = 4x$. Divide both sides by 4: $x = 45^{\circ}$. The supplement is $180-45 = 135^{\circ}$.

Answer:

The angle is $128^{\circ}$ and its supplement is $52^{\circ}$

7.