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

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Mar 9, 2018

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 $\left(x\right)$ - 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

$x + x = 114.$

$2 x = 114$

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

$\frac{2 x}{2} = \frac{114}{2}$

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 $123.$

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

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