If the ratio of angles of a quadrilateral is 2 : 7 : 2 : 7 then, quadrilateral will be.

Options

A. Rectangle
B. Square
C. Parallelogram
D. Rhombus

Answer

To solve the problem, we need to find out what type of quadrilateral has angles in the ratio of 2:7:2:7.

### Step-by-Step Solution:

1. **Understanding the Ratio**:
The angles of the quadrilateral are given in the ratio 2:7:2:7. Let's denote the angles as A, B, C, and D respectively. Therefore, we can express the angles in terms of a variable \( x \):
- Angle A = 2x
- Angle B = 7x
- Angle C = 2x
- Angle D = 7x

2. **Setting Up the Equation**:
The sum of the interior angles of a quadrilateral is always 360 degrees. Therefore, we can set up the following equation:
\[ A + B + C + D = 360 \]
Substituting the expressions for the angles, we get:
\[ 2x + 7x + 2x + 7x = 360 \]

3. **Combining Like Terms**:
Combine the terms on the left side:
\[ (2x + 7x + 2x + 7x) = 18x \]
So, the equation simplifies to:
\[ 18x = 360 \]

4. **Solving for x**:
To find the value of \( x \), divide both sides of the equation by 18:
\[ x = \frac{360}{18} = 20 \]

5. **Finding the Angles**:
Now that we have the value of \( x \), we can find the measures of each angle:
- Angle A = \( 2x = 2 \times 20 = 40^\circ \)
- Angle B = \( 7x = 7 \times 20 = 140^\circ \)
- Angle C = \( 2x = 40^\circ \)
- Angle D = \( 7x = 140^\circ \)

6. **Identifying the Type of Quadrilateral**:
We observe that angles A and C are equal (both 40 degrees) and angles B and D are equal (both 140 degrees). This indicates that opposite angles are equal, which is a property of a parallelogram.

### Conclusion:
Thus, the quadrilateral with angles in the ratio 2:7:2:7 is a **parallelogram**.