Question

the measure of one angle is eight times the measure of its supplement. the measure of the larger angle is:

Explanation:

Step1: Define the angles

Let one angle be $x$ and its supplement be $y$. We know that $x + y=180^{\circ}$ (by the definition of supplementary angles), and $x = 8y$.

Step2: Substitute and solve

Substitute $x = 8y$ into $x + y=180^{\circ}$. We get $8y+y=180^{\circ}$, which simplifies to $9y = 180^{\circ}$. Then $y=\frac{180^{\circ}}{9}=20^{\circ}$.

Step3: Find the larger angle

Since $x = 8y$, substituting $y = 20^{\circ}$, we get $x=8\times20^{\circ}=160^{\circ}$. The larger angle is $x$.

Answer:

$160$