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The given question asks to find the measure of angle \( \angle 1 \) in the triangle, where:

- \( \alpha = 35^\circ \)
- \( \beta = 89^\circ \)

From the diagram, the three angles in the triangle formed by \( \alpha \), \( \beta \), and \( \angle 1 \) must sum to 180° (since the sum of angles in a triangle is always 180°). Therefore, we can set up the equation:

\[
\alpha + \beta + \angle 1 = 180^\circ
\]

Substituting the values for \( \alpha \) and \( \beta \):

\[
35^\circ + 89^\circ + \angle 1 = 180^\circ
\]

Simplifying:

\[
124^\circ + \angle 1 = 180^\circ
\]

Solving for \( \angle 1 \):

\[
\angle 1 = 180^\circ - 124^\circ = 56^\circ
\]

Thus, \( \angle 1 = 56^\circ \), which corresponds to option **A**.

Would you like further details or have any other questions?

Here are 5 related questions to consider:
1. What are the rules for the sum of interior angles in a polygon?
2. How do you calculate the missing angle in any triangle if two angles are known?
3. Can the sum of angles in a triangle ever be more or less than 180°?
4. How does the concept of supplementary angles apply in this scenario?
5. How can you use exterior angles to find unknown interior angles?

**Tip:** In any triangle, knowing two angles immediately allows you to find the third by subtracting their sum from 180°.

What is m∠1 if α = 35° and β = 89°?

Learn how to find the measure of the third angle in a triangle when α = 35° and β = 89°. This problem demonstrates the Triangle Angle Sum Theorem and is suitable for students in Grades 7-9.

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