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)?

Answer: No!

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

Both pairs of angles pictured below are supplementary

supplementary not adjacent

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)

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Practice Problems

Problem 1

If $$m \angle 1 =32 $$ degrees, what is the $$m \angle 2 ? $$

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

Problem 2

$$ \angle c $$ and $$ \angle F $$ are supplementary. If $$m \angle C$$ is 25 degrees, what is the $$m \angle F$$?

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

Problem 3

If the ratio of two supplementary angles is 2:1, what is the measure of the larger angle?

First, since this is a ratio problem, 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

Problem 4

If the ratio of two supplementary angles is 8:1, what is the measure of the smaller angle?

First, since this is a ratio problem, 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 degrees
Answer: 20 degrees

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