Which of the following statements is incorrect about a kite?

Options

A. It is a quadrilateral with exactly two pairs of equal sides.
B. The diagonals are perpendicular to one another.
C. One of the diagonals bisect the other.
D. The measure of each angle of a kite is `120^@`.

Answer

To determine which statement about a kite is incorrect, we will analyze each option step by step.

### Step 1: Understand the properties of a kite
A kite is a type of quadrilateral that has specific properties:
- It has two pairs of adjacent sides that are equal.
- The diagonals intersect at right angles (90 degrees).
- One of the diagonals bisects the other diagonal.

### Step 2: Analyze each statement

**Statement 1:** A kite is a quadrilateral with exactly 2 pairs of sides equal.
- **Analysis:** This statement is true because a kite has two pairs of adjacent sides that are equal.

**Statement 2:** The diagonals of a kite are perpendicular to each other.
- **Analysis:** This statement is also true. One of the defining properties of a kite is that its diagonals intersect at right angles.

**Statement 3:** One of the diagonals bisects the other diagonal.
- **Analysis:** This statement is true as well. In a kite, one diagonal bisects the other diagonal.

**Statement 4:** The measurement of each angle of a kite is 120 degrees.
- **Analysis:** This statement is incorrect. The angles of a kite do not have a specific measurement of 120 degrees each. The sum of the angles in any quadrilateral is 360 degrees, and there is no requirement that the angles of a kite be equal or measure 120 degrees.

### Conclusion
After analyzing all the statements, we find that **Statement 4** is incorrect.

### Final Answer
The incorrect statement about a kite is: **The measurement of each angle of a kite is 120 degrees.**

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