Question

Two angles are complementary. The larger angle is 56° more than the smallerangle. Find the measures of both angles.

Answer 1

Answer:

smaller angle = 17°

larger angle = 73°

Step-by-step explanation:

Given:

larger angle = 56° more than the smaller angle

To find:

the measure of both angles

Complementary angles are angles that sum up to 90 degrees

smaller angle + larger angle = 90°

let the smaller angle = y

larger angle = 56 + y

`\begin{gathered} y\text{ + 56 + y = 90} \\ \\ 2y\text{ + 56 = 90} \\ \\ 2y\text{ = 90 -56} \\ \\ 2y\text{ = 34} \end{gathered}`
`\begin{gathered} divide\text{ both sides by 2:} \\ y\text{ = 34/2} \\ \\ y\text{ = 17} \\ \\ smaller\text{ angle = 17\degree} \\ \\ larger\text{ angle = 56 + 17 = 73\degree} \end{gathered}`