Question

two angles form a linear pair. the measure of one angle is twice the measure of the other angle. find the measure of each angle. the smaller angle measures °. the larger angle measures °.

Explanation:

Step1: Set up the equation

Let the measure of the smaller angle be $x$. Then the measure of the larger angle is $2x$. Since they form a linear - pair, $x + 2x=180^{\circ}$.

Step2: Solve the equation

Combining like terms, we get $3x = 180^{\circ}$. Dividing both sides by 3, $x=\frac{180^{\circ}}{3}=60^{\circ}$.

Step3: Find the measure of the larger angle

The larger angle is $2x$, so $2\times60^{\circ}=120^{\circ}$.

Answer:

The smaller angle measures $60^{\circ}$.
The larger angle measures $120^{\circ}$.