Triangle Exterior Angles worksheet with diagrams and problems for calculating angles.

Since I can't view or access images directly, I can't see the specific details of your image. However, if you describe the problem or provide the text and diagrams from the image (such as triangle configurations, given angles, or any labels), I can help you solve it step by step.

That said, based on the title "Triangle - Exterior Angles", I can assume this worksheet involves using the Exterior Angle Theorem of triangles. Here's a general explanation and solution approach for such problems:

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🔷 Exterior Angle Theorem

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

Also:
- The sum of the interior angles in any triangle is 180°.
- An exterior angle and its adjacent interior angle are supplementary (add up to 180°).

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Let’s go through typical problems like these:

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✔ Example Problem Type (a):

Given a triangle with two interior angles labeled, find the exterior angle at one vertex.

#### Example:
In triangle ABC:
- ∠A = 50°
- ∠B = 60°
- Find the exterior angle at C.

Solution:
1. First, find ∠C:
∠C = 180° – (∠A + ∠B) = 180° – (50° + 60°) = 70°
2. The exterior angle at C is supplementary to ∠C:
Exterior angle = 180° – 70° = 110°

Alternatively, use the Exterior Angle Theorem:
- Exterior angle at C = ∠A + ∠B = 50° + 60° = 110°

✔ So, the exterior angle is 110°.

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✔ Example Problem Type (b):

Find missing angles using the exterior angle.

#### Example:
In triangle ABC:
- ∠A = 40°
- Exterior angle at B = 110°
- Find ∠C

Solution:
1. Interior angle at B = 180° – 110° = 70°
2. Now, ∠C = 180° – (∠A + ∠B) = 180° – (40° + 70°) = 70°

Or using the exterior angle theorem:
- Exterior angle at B = ∠A + ∠C → 110° = 40° + ∠C → ∠C = 70°

✔ So, ∠C = 70°

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📝 General Steps to Solve These Problems:

1. Identify known angles (interior or exterior).
2. Use:
- Sum of interior angles = 180°
- Exterior angle = sum of two remote interior angles
- Adjacent interior + exterior = 180°
3. Plug in values and solve.

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If you can describe the specific triangles in your image (e.g., what angles are labeled, which ones are missing), I can walk you through each part exactly.

For example, say:
> "In part (a), triangle has angles 30° and 40°, and I need to find the exterior angle at the third vertex."

Then I’ll give the exact answer and reasoning.

Please provide the details, and I’ll solve it!