Question

the measure of an angle is 30 more than 5 times its supplement. find the measure of each angle. angle 1 = angle 2 =

Explanation:

Step1: Define the variable

Let the measure of the supplement be $x$. Then the measure of the angle is $5x + 30$.

Step2: Use the supplementary - angle property

Since two supplementary angles add up to 180 degrees, we have the equation $x+(5x + 30)=180$.

Step3: Simplify the equation

Combine like - terms: $6x+30 = 180$.

Step4: Solve for $x$

Subtract 30 from both sides: $6x=180 - 30=150$. Then divide both sides by 6: $x=\frac{150}{6}=25$.

Step5: Find the measure of the angle

The measure of the angle is $5x + 30$. Substitute $x = 25$ into this expression: $5\times25+30=125 + 30=155$.

Answer:

Angle 1 = 155
Angle 2 = 25