Question

an angle measures 174° less than the measure of its supplementary angle. what is the measure of each angle?

Explanation:

Step1: Define supplementary angles

Let the angle be $x$ and its supplementary angle be $y$. We know that $x + y=180^{\circ}$, and $x=y - 174^{\circ}$.

Step2: Substitute and solve

Substitute $x=y - 174^{\circ}$ into $x + y=180^{\circ}$. We get $(y - 174^{\circ})+y=180^{\circ}$. Combine like - terms: $2y-174^{\circ}=180^{\circ}$. Add $174^{\circ}$ to both sides: $2y=180^{\circ}+174^{\circ}=354^{\circ}$. Then divide both sides by 2: $y = 177^{\circ}$.

Step3: Find the other angle

Since $x=y - 174^{\circ}$, substitute $y = 177^{\circ}$ into it. So $x=177^{\circ}-174^{\circ}=3^{\circ}$.

Answer:

$3$, $177$