Triangle - Exterior Angles Worksheet Collection For Teaching ... - Free Printable

Let's solve each problem using the Exterior Angle Theorem, which states:

> The measure of an exterior angle of a triangle is equal to the sum of the measures of the two non-adjacent (remote) interior angles.

We’ll go through each problem one by one.

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Problem 1:

Given:
- Triangle $ \triangle QRS $
- $ \angle R = 80^\circ $
- Exterior angle at $ S $ is $ 150^\circ $
- Find $ x = \angle Q $

Step-by-step:

The exterior angle at $ S $ is $ 150^\circ $. This exterior angle is formed by extending side $ RS $ to point $ E $, so:
$$
\text{Exterior angle} = \angle Q + \angle R
$$
$$
150^\circ = x + 80^\circ
$$
$$
x = 150^\circ - 80^\circ = 70^\circ
$$

✔ Answer: $ x = 70^\circ $ → Color: blue

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Problem 2:

Given:
- Triangle $ \triangle VUT $
- $ \angle V = 50^\circ $
- Exterior angle at $ T $ is $ 115^\circ $
- Find $ x = \angle U $

Step-by-step:

Exterior angle at $ T $ is $ 115^\circ $, so:
$$
\text{Exterior angle} = \angle V + \angle U
$$
$$
115^\circ = 50^\circ + x
$$
$$
x = 115^\circ - 50^\circ = 65^\circ
$$

✔ Answer: $ x = 65^\circ $ → Color: teal

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Problem 3:

Given:
- Triangle $ \triangle VTU $
- $ \angle T = 80^\circ $
- $ \angle U = 40^\circ $
- Find $ x = \angle V $

Wait — this is not an exterior angle problem directly. But we can use Triangle Angle Sum Theorem:
$$
\angle V + \angle T + \angle U = 180^\circ
$$
$$
x + 80^\circ + 40^\circ = 180^\circ
$$
$$
x = 180^\circ - 120^\circ = 60^\circ
$$

But let’s check if there's an exterior angle involved. Point $ B $ is above $ V $, and ray $ BV $ extends upward. So, angle at $ V $ is between $ BV $ and $ VT $, but no exterior angle is labeled.

Actually, the question asks for $ x $ at vertex $ V $, and it's just the interior angle. So yes, we use the triangle sum.

✔ Answer: $ x = 60^\circ $ → Color: purple

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Problem 4:

Given:
- Triangle $ \triangle ABC $
- $ \angle C = 20^\circ $
- Exterior angle at $ A $ is $ 125^\circ $
- Find $ x = \angle B $

Step-by-step:

Exterior angle at $ A $ is $ 125^\circ $. This means:
$$
\text{Exterior angle at } A = \angle B + \angle C
$$
$$
125^\circ = x + 20^\circ
$$
$$
x = 125^\circ - 20^\circ = 105^\circ
$$

✔ Answer: $ x = 105^\circ $ → Color: pink

---

Problem 5:

Given:
- Triangle $ \triangle ABC $
- $ \angle B = 45^\circ $
- Exterior angle at $ C $ is $ 140^\circ $
- Find $ x = \angle A $

Step-by-step:

Exterior angle at $ C $ is $ 140^\circ $. So:
$$
\text{Exterior angle at } C = \angle A + \angle B
$$
$$
140^\circ = x + 45^\circ
$$
$$
x = 140^\circ - 45^\circ = 95^\circ
$$

✔ Answer: $ x = 95^\circ $ → Color: black

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Problem 6:

Given:
- Triangle $ \triangle CDE $
- $ \angle D = 110^\circ $
- Exterior angle at $ C $ is $ 140^\circ $
- Find $ x = \angle E $

Step-by-step:

Exterior angle at $ C $ is $ 140^\circ $. So:
$$
\text{Exterior angle at } C = \angle D + \angle E
$$
$$
140^\circ = 110^\circ + x
$$
$$
x = 140^\circ - 110^\circ = 30^\circ
$$

✔ Answer: $ x = 30^\circ $ → Color: blue

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✔ Final Answers Summary:

| Problem | $ x $ | Color |
|--------|--------|-------|
| 1 | $ 70^\circ $ | blue |
| 2 | $ 65^\circ $ | teal |
| 3 | $ 60^\circ $ | purple |
| 4 | $ 105^\circ $ | pink |
| 5 | $ 95^\circ $ | black |
| 6 | $ 30^\circ $ | blue |

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🎨 Coloring Instructions:

- Use blue for problems 1 and 6
- Use teal for problem 2
- Use purple for problem 3
- Use pink for problem 4
- Use black for problem 5

Now you can color the picture accordingly!

Let me know if you'd like a visual explanation or help with coloring!