Question

Two angles are supplementary. The larger angle is 66 degrees larger then the smaller angle. Find the measure of both angles?

Answer 1

The answer is `57° and 123°`.

Explanation:

A supplementary angle is an angle that equals `180°`. So now we know that the two angles added together will give us `180°`, we can use this to check at the end.

Let's call the smaller angle `x`
We also know that the larger number is `66°` more than the smaller. This gives us:

`x + x + 66° = 180°`.

x is equal to the smaller angle, and the second angle is `( x)` - the smaller number with an extra `66°`, giving us the difference.

Now we can simplify this by subtracting `66°` from both sides.

`x+x+66°-66° = 180°-66°`

(balancing the equation) and get

`x + x = 114.`

`2x = 114`

Next, we can divide `114` by `2` as there are `2x's`,

`(2x)/2 = 114/2`

giving us `x=57`.

`57` is, therefore, the smaller angle.

To get the larger angle we can either subtract: `180°-57 = 123°`

or add: `66° + 5° = 123°`

Both answers give us `123.`

To check our answer, we can add:

`57° + 123° =180°`, and proving the answer.