Question

name gracie b.k.
practice
example 1

1. find the measures of two supplementary angles if the difference between the measures of the two angles is 35°.
2. ∠e and ∠f are complementary. the measure of ∠e is 54° more than the measure of ∠f. find the measure of each angle.
3. the measure of an angle’s supplement is 76° less than the measure of the angle. find the measures of the angle and its supplement.
4. ∠q and ∠r...

Explanation:

Problem 1:

Step1: Define variables

Let the smaller angle be $x$, then the larger angle is $x + 35$. Since they are supplementary, their sum is $180^\circ$. So, $x+(x + 35)=180$.

Step2: Solve the equation

Simplify: $2x+35 = 180$. Subtract 35: $2x=180 - 35=145$. Divide by 2: $x=\frac{145}{2}=72.5^\circ$. Larger angle: $72.5 + 35 = 107.5^\circ$.

Step1: Define variables

Let $m\angle F=x$, then $m\angle E=x + 54$. Since they are complementary, $x+(x + 54)=90$.

Step2: Solve the equation

Simplify: $2x+54 = 90$. Subtract 54: $2x=90 - 54 = 36$. Divide by 2: $x = 18^\circ$. $m\angle E=18 + 54 = 72^\circ$.

Step1: Define variables

Let the angle be $x$, its supplement is $180 - x$. Given that $180 - x=x - 76$.

Step2: Solve the equation

Add $x$ to both sides: $180=2x - 76$. Add 76: $2x=180 + 76 = 256$. Divide by 2: $x = 128^\circ$. Supplement: $180 - 128 = 52^\circ$.

Answer:

The two angles are $72.5^\circ$ and $107.5^\circ$.

Problem 2: