Which of the following statements is incorrect?

Options

A. Each diagonal of a quadrilateral divides it into two triangles.
B. Each side of a quadrilateral is less than the sum of the remaining three sides.
C. A quadrilateral can have atmost three angles.
D. A quadrilateral has two diagonals.

Answer

To determine which statement is incorrect, let's analyze each statement one by one.

### Step 1: Analyze the first statement
**Statement 1:** Each diagonal of a quadrilateral divides it into two triangles.

- A diagonal of a quadrilateral connects two non-adjacent vertices. When you draw a diagonal, it creates two triangles within the quadrilateral.
- **Conclusion:** This statement is **correct**.

### Step 2: Analyze the second statement
**Statement 2:** Each side of a quadrilateral is less than the sum of the remaining three sides.

- This statement is a restatement of the triangle inequality theorem, which applies to any polygon. In a quadrilateral, each side must be less than the sum of the other three sides to ensure that the shape can exist.
- **Conclusion:** This statement is **correct**.

### Step 3: Analyze the third statement
**Statement 3:** Each side of a quadrilateral is less than the sum of the remaining three sides.

- This statement is identical to the second statement, which we have already established as correct.
- **Conclusion:** This statement is also **correct**.

### Step 4: Identify any incorrect statements
After analyzing all three statements, we find that all the statements provided are correct. However, the repetition of the third statement may indicate a mistake in the transcription or a misunderstanding.

### Final Conclusion
Since all statements analyzed are correct, there is no incorrect statement among the ones provided.