https://file.aiquickdraw.com/mathbot/file/17285966575729bsgui2p.jpg

To solve for \( m \angle 1 \) in the figure provided:

### Step 1: Analyze the triangle.
- The triangle in question is a right triangle, as indicated by the small square marking at the vertex near \( \angle 2 \), meaning \( \angle 2 = 90^\circ \).
- The given angles are:
  - \( \angle 3 = 50^\circ \),
  - \( \angle 1 = ? \) (this is what we're solving for),
  - \( \angle 2 = 90^\circ \) (as it's a right triangle).

### Step 2: Use the triangle angle sum property.
The sum of the interior angles in any triangle is always \( 180^\circ \). Therefore, in this right triangle, the sum of the angles must satisfy the equation:

\[
\angle 1 + \angle 2 + \angle 3 = 180^\circ
\]

Substitute the known values:

\[
\angle 1 + 90^\circ + 50^\circ = 180^\circ
\]

### Step 3: Solve for \( \angle 1 \).
\[
\angle 1 = 180^\circ - 90^\circ - 50^\circ
\]
\[
\angle 1 = 40^\circ
\]

Thus, \( m \angle 1 = 40^\circ \).

The correct answer is **40**.

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Would you like further clarification on any step? Here are some related questions:

1. What is the sum of interior angles in a triangle, and how does it apply to different triangle types?
2. How do you identify a right triangle based on the markings in a figure?
3. Can the Pythagorean theorem help in solving angle problems in right triangles?
4. What are exterior angles, and how are they related to the interior angles of a triangle?
5. How can trigonometric ratios be used to find angles in right triangles?

**Tip**: Always remember that the sum of angles in any triangle, whether right or not, is 180°.

What is the measure of angle 1 in a right triangle where angle 3 is 50° and angle 2 is 90°?

Learn how to calculate the missing angle in a right triangle where one angle is 50° and another is 90°. This geometry problem uses the triangle angle sum theorem, suitable for students in Grades 6-8.

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