The measures of 3 diffferent angles of one of the set squares are _____.

Options

A. `90^(@) - 45 ^(@) - 30^(@)`
B. `30^(@) -90^(@) -60^(@)`
C. `70^(@)-50^(@)-60^(@)`
D. None of these

Answer

To solve the problem regarding the measures of the three different angles of one of the set squares, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Types of Set Squares**:
- A set square typically consists of two types of triangles: an isosceles triangle and a right-angled triangle.

2. **Understand the Properties of the Triangles**:
- **Isosceles Triangle**: In an isosceles triangle, two sides are equal, and the angles opposite those sides are also equal.
- **Right-Angled Triangle**: In a right-angled triangle, one angle measures 90 degrees.

3. **Determine the Angles**:
- For the isosceles triangle, let's assume the angles are \( x, x, \) and \( 180 - 2x \).
- For the right-angled triangle, one angle is \( 90^\circ \), and the other two angles must add up to \( 90^\circ \) (since the sum of angles in a triangle is \( 180^\circ \)).

4. **Check Possible Angle Combinations**:
- The angles must satisfy the triangle sum property (the sum of the angles in a triangle is \( 180^\circ \)).
- For example, if we consider the angles \( 30^\circ, 60^\circ, \) and \( 90^\circ \) for the right-angled triangle, we find:
- \( 30 + 60 + 90 = 180^\circ \)

5. **Select the Correct Option**:
- Based on the options given, we check which combination of angles satisfies the triangle sum property.
- The angles \( 30^\circ, 60^\circ, \) and \( 90^\circ \) meet the criteria.

6. **Conclusion**:
- Therefore, the measures of the three different angles of one of the set squares are \( 30^\circ, 60^\circ, \) and \( 90^\circ \).

### Final Answer:
The measures of the three different angles of one of the set squares are \( 30^\circ, 60^\circ, \) and \( 90^\circ \).

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