Grade 7 math worksheet on exterior angles of a triangle, with problems for calculating unknown angles.

Let's solve each part of the Exit Task (Exterior angles of a triangle) step by step.

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🔷 Must Know:

#### 1. First Triangle
- Interior angles: 50° and 70°
- Exterior angle $ x $ is adjacent to the third interior angle.
- The exterior angle equals the sum of the two opposite interior angles.

$$
x = 50^\circ + 70^\circ = 120^\circ
$$

✔ $ x = 120^\circ $

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#### 2. Second Triangle
- Interior angles: 65° and 45°
- Exterior angle $ x $ is adjacent to the third interior angle.

$$
x = 65^\circ + 45^\circ = 110^\circ
$$

✔ $ x = 110^\circ $

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🔷 Good to Know:

#### 3. Triangle ABC with D-B extended
Given:
- ∠C = 62°
- ∠A = 51°
- Find $ x $ (exterior angle at B), and $ y $ (interior angle at B)

First, find interior angle $ \angle B $:

Sum of angles in triangle = 180°

$$
\angle B = 180^\circ - 62^\circ - 51^\circ = 67^\circ
$$

So $ y = 67^\circ $

Now, exterior angle $ x $ at B is supplementary to $ y $:

$$
x = 180^\circ - 67^\circ = 113^\circ
$$

✔ $ x = 113^\circ $, $ y = 67^\circ $

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#### 4. Triangle ABC with D-B extended
Given:
- ∠C = 70°
- Exterior angle at B = 120° → so interior angle $ \angle B = 180^\circ - 120^\circ = 60^\circ $
- Find $ x $ (angle at A), $ y $ (angle at B)

Wait — here $ y $ is labeled as $ \angle B $, which we already found:

$$
y = 60^\circ
$$

Now find $ x = \angle A $:

$$
\angle A = 180^\circ - \angle B - \angle C = 180^\circ - 60^\circ - 70^\circ = 50^\circ
$$

✔ $ x = 50^\circ $, $ y = 60^\circ $

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🔷 Fun to Know:

Triangle ABC with:
- ∠C = $ 3y^\circ $
- ∠B = $ 5y^\circ $
- Exterior angle at B = $ 7y^\circ $
- ∠A = $ x^\circ $

We are to find:
- $ x $
- $ y $
- $ \angle A $
- $ \angle B $
- $ \angle C $
- exterior $ \angle B $

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Step 1: Use the exterior angle theorem:
> Exterior angle at B = sum of two opposite interior angles

So:
$$
\text{Exterior } \angle B = \angle A + \angle C
$$
$$
7y = x + 3y
$$

But also, sum of interior angles in triangle:
$$
\angle A + \angle B + \angle C = 180^\circ
$$
$$
x + 5y + 3y = 180^\circ
\Rightarrow x + 8y = 180^\circ \quad \text{(Equation 1)}
$$

From earlier:
$$
7y = x + 3y \Rightarrow x = 7y - 3y = 4y \quad \text{(Equation 2)}
$$

Substitute into Equation 1:
$$
4y + 8y = 180^\circ \Rightarrow 12y = 180^\circ \Rightarrow y = 15^\circ
$$

Now:
- $ y = 15^\circ $
- $ x = 4y = 60^\circ $
- $ \angle A = x = 60^\circ $
- $ \angle B = 5y = 75^\circ $
- $ \angle C = 3y = 45^\circ $
- Exterior $ \angle B = 7y = 105^\circ $

✔ All values:

- $ x = 60^\circ $
- $ y = 15^\circ $
- $ \angle A = 60^\circ $
- $ \angle B = 75^\circ $
- $ \angle C = 45^\circ $
- exterior $ \angle B = 105^\circ $

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✔ Final Answers:

#### Must Know:
- $ x = 120^\circ $
- $ x = 110^\circ $

#### Good to Know:
- $ x = 113^\circ $, $ y = 67^\circ $
- $ x = 50^\circ $, $ y = 60^\circ $

#### Fun to Know:
- $ x = 60^\circ $
- $ y = 15^\circ $
- $ \angle A = 60^\circ $
- $ \angle B = 75^\circ $
- $ \angle C = 45^\circ $
- exterior $ \angle B = 105^\circ $

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📌 Summary of All Answers (Numerical Values Only):

Must Know:
- $ x = 120 $
- $ x = 110 $

Good to Know:
- $ x = 113 $, $ y = 67 $
- $ x = 50 $, $ y = 60 $

Fun to Know:
- $ x = 60 $
- $ y = 15 $
- $ \angle A = 60 $
- $ \angle B = 75 $
- $ \angle C = 45 $
- exterior $ \angle B = 105 $

✔ All solved!