Question

two angles form a linear pair. the measure of one angle is $\frac{1}{3}$ the measure of the other angle. find the measure of each angle. the smaller angle measures $square^{circ}$. the larger angle measures $square^{circ}$.

Explanation:

Step1: Set up the equation

Let the larger angle be $x$ degrees. Then the smaller angle is $\frac{1}{3}x$ degrees. Since they form a linear - pair, their sum is 180 degrees. So, $x+\frac{1}{3}x = 180$.

Step2: Combine like - terms

Combining the terms on the left - hand side, we get $\frac{3x + x}{3}=180$, which simplifies to $\frac{4x}{3}=180$.

Step3: Solve for $x$

Multiply both sides of the equation by $\frac{3}{4}$: $x = 180\times\frac{3}{4}=135$.

Step4: Find the measure of the smaller angle

The smaller angle is $\frac{1}{3}x$. Substitute $x = 135$ into it, we get $\frac{1}{3}\times135 = 45$.

Answer:

The smaller angle measures $45^{\circ}$.
The larger angle measures $135^{\circ}$.