Question

problem solving
two angles are supplementary if their sum is 180. the larger angle measures four degrees more than seven times the measure of a smaller angle. x represents the measure of the smaller angle and the two angles are supplementary, find the measure of each angle.
the smaller angle is ____ °
the larger angle is ____ °
x + (7x + 4) = 180

Explanation:

Step1: Combine like - terms

$x+(7x + 4)=180$ simplifies to $8x+4 = 180$.

Step2: Subtract 4 from both sides

$8x+4-4=180 - 4$, so $8x=176$.

Step3: Divide both sides by 8

$\frac{8x}{8}=\frac{176}{8}$, then $x = 22$.

Step4: Find the larger angle

The larger angle is $7x+4$. Substitute $x = 22$ into it, $7\times22+4=154 + 4=158$.

Answer:

The smaller angle is $22^{\circ}$.
The larger angle is $158^{\circ}$.