Question

an angle measures 122° more than the measure of its supplementary angle. what is the measure of each angle?

Explanation:

Step1: Let the measure of the angle be $x$ and its supplementary angle be $y$.

We know that $x + y=180^{\circ}$ (by the definition of supplementary angles), and $x=y + 122^{\circ}$.

Step2: Substitute $x=y + 122^{\circ}$ into $x + y=180^{\circ}$.

$(y + 122^{\circ})+y=180^{\circ}$.

Step3: Simplify the equation.

$2y+122^{\circ}=180^{\circ}$.
Then $2y=180^{\circ}- 122^{\circ}=58^{\circ}$.

Step4: Solve for $y$.

$y=\frac{58^{\circ}}{2}=29^{\circ}$.

Step5: Solve for $x$.

Since $x=y + 122^{\circ}$, then $x=29^{\circ}+122^{\circ}=151^{\circ}$.

Answer:

The angles are $151^{\circ}$ and $29^{\circ}$