#### 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°.

**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°.

to each other (ie adjacent)?

**Answer: ** No!

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.

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 |
---|---|

∠ B | 90 |

Drag The Circle To Start The Demonstration

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

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

**Answer: **120 degrees

First, since this is a ratio problem, we will let the larger angle be 8x and the smaller angle x. We know that 8x + 1x = 180 , so now, let's first solve for x:

$$ 9x = 180° \\ x = \frac{180°}{9} = 20° $$

Now, the smaller angle is the 1x which is 1(20°) = 20°

**Answer: **20°