Question

What are the supplement and complement of the numbers below:

72 degrees
125 degrees
-45degrees

Answer 1

Part 1) 72 degrees

complement
`18\°` and supplement
`108\°`

Part 2) 125 degrees

complement
`-35\°` and supplement
`55\°`

Part 3) -45 degrees

complement
`135\°` and supplement
`225\°`

Explanation:

we know that

Two angles are complementary if their sum is equal to 90 degrees

Two angles are supplementary if their sum is equal to 180 degrees

Part 1) 72 degrees

Let

x-----> the complement

y-----> the supplement

so

Find the complement

`x+72\°=90\°`

solve for x

`x=90\°-72\°=18\°`

Find the supplement

`y+72\°=180\°`

solve for y

`y=180\°-72\°=108\°`

Part 2) 125 degrees

Let

x-----> the complement

y-----> the supplement

so

Find the complement

`x+125\°=90\°`

solve for x

`x=90\°-125\°=-35\°`

Find the supplement

`y+125\°=180\°`

solve for y

`y=180\°-125\°=55\°`

Part 3) -45 degrees

Let

x-----> the complement

y-----> the supplement

so

Find the complement

`x+(-45\°)=90\°`

solve for x

`x=90\°+45\°=135\°`

Find the supplement

`y+(-45\°)=180\°`

solve for y

`y=180\°+45\°=225\°`