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The image you've uploaded shows a triangle with three exterior angles labeled \( w \), \( x \), and \( y \), and an interior angle labeled \( z = 70^\circ \). To solve for the unknown angles, let's use the following properties:

### 1. **Exterior Angle Theorem**:
Each exterior angle of a triangle is equal to the sum of the two non-adjacent interior angles.

### 2. **Sum of Interior Angles of a Triangle**:
The sum of the interior angles of a triangle is always \(180^\circ\).

Let's break this down:

#### Step 1: Identify relationships between angles.
- The angle \( w \) is an exterior angle, and it is supplementary to the interior angle adjacent to it. This means:
  \[
  w + z = 180^\circ
  \]
  \[
  w + 70^\circ = 180^\circ
  \]
  Solving for \( w \):
  \[
  w = 180^\circ - 70^\circ = 110^\circ
  \]

- The angle \( x = 130^\circ \) is given as an exterior angle. The adjacent interior angle to this is:
  \[
  \text{Interior angle adjacent to } x = 180^\circ - 130^\circ = 50^\circ
  \]

- The angle \( y = 80^\circ \) is also an exterior angle. The adjacent interior angle to this is:
  \[
  \text{Interior angle adjacent to } y = 180^\circ - 80^\circ = 100^\circ
  \]

#### Step 2: Calculate interior angles.
- We already know that \( z = 70^\circ \).
- The interior angle adjacent to \( x \) is \( 50^\circ \).
- The interior angle adjacent to \( y \) is \( 100^\circ \).

#### Step 3: Verification (sum of interior angles).
The sum of the interior angles should be:
\[
70^\circ + 50^\circ + 100^\circ = 220^\circ
\]
This result is not possible because it exceeds \(180^\circ\), meaning we should reconsider this approach. The structure of the triangle might involve alternate properties of linear angles and their relationships.

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The image shows a triangle with exterior angles labeled w, x, and y, and an interior angle labeled z = 70°. Solve for the unknown angles.

Learn how to solve for unknown exterior and interior angles in a triangle using the Exterior Angle Theorem and angle sum properties. This problem is suitable for high school geometry students.

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