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In this image, the question asks for the measure of angle \( \angle 1 \), given that two other angles of the triangle are labeled \( 97^\circ \) and the exterior angle \( 134^\circ \).

### Explanation:
This problem uses the **exterior angle theorem**, which states:
\[
\text{Exterior angle} = \text{Sum of the two non-adjacent interior angles}
\]

Here, the exterior angle is \( 134^\circ \), and one of the non-adjacent interior angles is \( 97^\circ \). Let \( m \angle 1 \) be the unknown interior angle that we are solving for.

According to the theorem:
\[
134^\circ = 97^\circ + m \angle 1
\]
To solve for \( m \angle 1 \), subtract \( 97^\circ \) from both sides:
\[
m \angle 1 = 134^\circ - 97^\circ = 37^\circ
\]

So, \( m \angle 1 = 37^\circ \).

Would you like more details or have any other questions?

Here are 5 related questions you might find helpful:
1. What is the exterior angle theorem?
2. How can you calculate missing angles in a triangle?
3. How do you find the third angle of a triangle given two angles?
4. What is the sum of interior angles in a triangle?
5. How are interior and exterior angles related in polygons?

**Tip:** When solving for angles in a triangle, always check if any angle relationships or theorems (like the exterior angle theorem) can simplify the process.

What is the measure of angle 1 (m∠1) in the triangle, given that one of the interior angles is 97° and the exterior angle is 134°?

Solve for the measure of angle 1 (m∠1) in a triangle where one interior angle is 97° and the exterior angle is 134°, using the exterior angle theorem. This problem is suitable for students in Grades 7-9, and demonstrates key concepts in geometry and triangle angle relationships.

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