If two angles of a triangle are `21^@ and 38^@`, then the triangle is

Options

A. Right-angled triangle
B. Acute-angled triangle
C. Obtuse-angled triangle
D. Isosceles triangle

Answer

To determine the type of triangle based on the given angles, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Given Angles**: We have two angles of the triangle, which are 21° and 38°.

2. **Calculate the Third Angle**:
- We know that the sum of the angles in a triangle is always 180°.
- Let the third angle be \( x \).
- Therefore, we can set up the equation:
\[ 21° + 38° + x = 180° \]

3. **Simplify the Equation**:
- First, add the two given angles:
\[ 21° + 38° = 59° \]
- Now substitute this back into the equation:
\[ 59° + x = 180° \]

4. **Solve for \( x \)**:
- To find \( x \), subtract 59° from both sides:
\[ x = 180° - 59° \]
- Calculate the value:
\[ x = 121° \]

5. **Determine the Type of Triangle**:
- We now have all three angles: 21°, 38°, and 121°.
- Since one of the angles (121°) is greater than 90°, the triangle is classified as an **obtuse triangle**.

### Conclusion:
The triangle with angles 21°, 38°, and 121° is an **obtuse triangle**.

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