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# Supplementary Angles

#### What are supplementary angles?

Answer: Supplementary angles are angles whose sum is 180 °

No matter how large or small angles 1 and 2 on the left become, the two angles remain supplementary which means that they add up to 180°.

#### Do supplementary angles need to be next to each other (ie adjacent)?

Supplementary angles do not need to be adjacent angles (angles next to one another).

Both pairs of angles pictured below are supplementary.

Angles that are supplementary and adjacent are known as a linear pair.

### Interactive Supplementary Angles

Click and drag around the points below to explore and discover the rule for vertical angles on your own.

You can click and drag points A, B, and C.

(Full Size Interactive Supplementary Angles)

 ∠ A 90 90
Drag The Circle To Start The Demonstration

### Practice Problems

##### Problem 1

$$m \angle 1 + m \angle 2 = 180° \\ 32° + m \angle 2 = 180° \\ m \angle 2 = 180°-32° \\ m \angle 2 = 148°$$

##### Problem 2

$$m \angle c + m \angle F = 180° \\ 25° + m \angle F = 180° \\ m \angle F = 180°-25° = 155°$$

##### Problem 3

First, since this is a ratio problem, we will let the larger angle be 2x and the smaller angle x. We know that $$2x + 1x = 180$$ , so now, let's first solve for x:

$$3x = 180° \\ x = \frac{180°}{3} = 60°$$

Now, the larger angle is the 2x which is 2(60) = 120 degrees
$$9x = 180° \\ x = \frac{180°}{9} = 20°$$