Question

an angle measures 38° more than the measure of its supplementary angle. what is the measure of each angle?

Explanation:

Step1: Define the relationship

Let one angle be $x$ and its supplementary angle be $y$. We know that $x + y=180^{\circ}$ and $x=y + 38^{\circ}$.

Step2: Substitute and solve

Substitute $x=y + 38^{\circ}$ into $x + y=180^{\circ}$, we get $(y + 38^{\circ})+y=180^{\circ}$. Combine like - terms: $2y+38^{\circ}=180^{\circ}$. Then $2y=180^{\circ}-38^{\circ}=142^{\circ}$, so $y = 71^{\circ}$.

Step3: Find the other angle

Since $x=y + 38^{\circ}$, then $x=71^{\circ}+38^{\circ}=109^{\circ}$.

Answer:

$109$ and $71$