If the angles A, B, C and D of a quadrilateral ABCD are in the ratio 11 : 19 : 21 : 9, then which of the following is correct?

Options

A. ABCD is a square
B. ABCD is a trapezium with AD || BC
C. ABCD is a rectangle
D. Can't be determined

Answer

To solve the problem, we need to find the angles A, B, C, and D of quadrilateral ABCD given that they are in the ratio 11:19:21:9.

### Step-by-Step Solution:

1. **Set Up the Ratios**:
Let the angles A, B, C, and D be represented as:
- A = 11x
- B = 19x
- C = 21x
- D = 9x

2. **Sum of Angles in a Quadrilateral**:
We know that the sum of the angles in any quadrilateral is 360 degrees. Therefore, we can write the equation:
\[ A + B + C + D = 360 \]
Substituting the expressions for A, B, C, and D:
\[ 11x + 19x + 21x + 9x = 360 \]

3. **Combine Like Terms**:
Combine the terms on the left side:
\[ (11 + 19 + 21 + 9)x = 360 \]
\[ 60x = 360 \]

4. **Solve for x**:
Divide both sides by 60 to find the value of x:
\[ x = \frac{360}{60} = 6 \]

5. **Calculate Each Angle**:
Now substitute x back into the expressions for each angle:
- A = 11x = 11 * 6 = 66 degrees
- B = 19x = 19 * 6 = 114 degrees
- C = 21x = 21 * 6 = 126 degrees
- D = 9x = 9 * 6 = 54 degrees

6. **Conclusion**:
The angles of quadrilateral ABCD are:
- A = 66 degrees
- B = 114 degrees
- C = 126 degrees
- D = 54 degrees