https://file.aiquickdraw.com/mathbot/file/1725376663865mdv7l32o.jpg

I see that you've uploaded a photo of a math problem displayed on a screen. Let me extract and analyze the content.

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The problem appears to involve a right triangle, and it is asking you to find the value of angle \( y \).

The triangle is labeled as follows:
- The right angle is at \( C \).
- Angle \( A \) is \( 32^\circ \).
- Angle \( y \) is at \( B \).
- There might be some other given information regarding the sides or angles.

The problem provides four answer choices:
- \( 58^\circ \)
- \( 138^\circ \)
- \( 32^\circ \)
- \( 122^\circ \)

### Solution:

Since this is a right triangle, the sum of the angles in any triangle is \( 180^\circ \). In a right triangle:
- One of the angles is \( 90^\circ \).
- The sum of the other two angles must be \( 90^\circ \) (since \( 180^\circ - 90^\circ = 90^\circ \)).

Given:
- \( \angle A = 32^\circ \).
- \( \angle y = \angle B \).

To find \( y \), subtract the given angle from \( 90^\circ \):

\[
y = 90^\circ - 32^\circ = 58^\circ
\]

Thus, the correct answer should be **\( 58^\circ \)**.

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Would you like more details on how to approach similar problems, or do you have any specific questions?

### Related Questions:
1. How do you find the angles in any triangle if all sides are given?
2. How can you determine the area of a triangle given two sides and the included angle?
3. What is the relationship between the sides and angles in a right triangle?
4. How does the Pythagorean theorem apply to this triangle?
5. Can trigonometric ratios be used to find unknown angles or sides in a triangle?

**Tip:** Always double-check that the sum of the angles in any triangle equals \( 180^\circ \) to ensure your calculations are correct.

Given a right triangle ABC, where angle A = 32° and angle C is 90°, find the value of angle B (angle y).

This page explains how to find the missing angle B (angle y) in a right triangle where angle A is 32° and angle C is 90°. The solution uses the triangle angle sum theorem, suitable for students in Grades 6-8.

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