Question

the ratio of the measure of an angle to the measure of its complement is 2:7. find the measure of each angle. the smaller angle measures °. the larger angle measures °.

Explanation:

Step1: Define the angles

Let the measure of the angle be $2x$ and the measure of its complement be $7x$.

Step2: Use the property of complementary - angles

Since complementary angles add up to $90^{\circ}$, we have the equation $2x + 7x=90$.

Step3: Solve the equation

Combining like - terms, we get $9x = 90$. Then, dividing both sides by 9, we have $x=\frac{90}{9}=10$.

Step4: Find the measure of each angle

The measure of the smaller angle (the given angle) is $2x = 2\times10 = 20^{\circ}$.
The measure of the larger angle (the complement) is $7x=7\times10 = 70^{\circ}$.

Answer:

The smaller angle measures $20^{\circ}$.
The larger angle measures $70^{\circ}$.