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The problem provides:

1. \( m \angle 2 = 41^\circ \)
2. A right angle at the vertex, meaning the two angles \( \angle 1 \) and \( \angle 2 \) must add up to \( 90^\circ \) since they form a right angle.

To find \( m \angle 1 \):
\[
m \angle 1 = 90^\circ - m \angle 2
\]
Substitute \( m \angle 2 = 41^\circ \):
\[
m \angle 1 = 90^\circ - 41^\circ = 49^\circ
\]

### Answer:
\( m \angle 1 = 49^\circ \)

Would you like further details or explanations?

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Here are some related questions to explore:

1. How would you calculate the other angle in any right-angled triangle if one angle is known?
2. What are complementary angles, and why are they relevant here?
3. How would this calculation differ if it was not a right angle at the vertex?
4. What are the properties of angles in different types of triangles?
5. How can trigonometry be applied if only the angle measures are given?

**Tip:** In any right triangle, the two non-right angles are complementary, meaning they add up to \( 90^\circ \).

In the figure below, m∠2 = 41°. Find m∠1.

Learn how to find the measure of m∠1 given that m∠2 = 41° in a right angle setup. This solution uses complementary angles to solve for unknown angles, ideal for students in Grades 6-8.

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