Three angles of a quadrilateral are `30^(@),150^(@)` and `100^(@)`. Find the fourth angle.

Answer

To find the fourth angle of the quadrilateral when three angles are given, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Given Angles**:
The angles provided are:
- First angle = 30°
- Second angle = 150°
- Third angle = 100°

2. **Recall the Sum of Angles in a Quadrilateral**:
The sum of all angles in a quadrilateral is always 360°.

3. **Set Up the Equation**:
Let the fourth angle be represented as \( X \). Therefore, we can write the equation:
\[ 30° + 150° + 100° + X = 360° \]

4. **Calculate the Sum of the Given Angles**:
First, add the three known angles:
\[ 30° + 150° = 180° \]
Then, add the third angle:
\[ 180° + 100° = 280° \]

5. **Substitute the Sum Back into the Equation**:
Now, substitute the sum of the known angles back into the equation:
\[ 280° + X = 360° \]

6. **Solve for \( X \)**:
To find \( X \), subtract 280° from both sides of the equation:
\[ X = 360° - 280° \]
\[ X = 80° \]

7. **Conclusion**:
The fourth angle of the quadrilateral is \( 80° \).

### Final Answer:
The fourth angle is \( 80° \).

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