Assertion : A quadrilateral has 4 and 2 angle and 4 diagonals.
Reason : A quadrilateral is a polygon made up of line segments.

Options

A. If both assertion and reason are true and reason is the correct explanation of assertion.
B. If both assertion and reason are true but reason is not the correct explanation of assertion.
C. If assertion is true but reason is false.
D. If assertion is false but reason is true.

Answer

To solve the assertion and reason question regarding quadrilaterals, we will analyze both statements step by step.

### Step 1: Analyze the Assertion
The assertion states: "A quadrilateral has 4 angles and 4 diagonals."

- A quadrilateral is defined as a polygon with four sides.
- By definition, a quadrilateral has exactly **4 angles** (one at each vertex).
- However, the assertion claims that it has **4 diagonals**.

To find the number of diagonals in a quadrilateral, we can use the formula for the number of diagonals in a polygon, which is given by:

\[ \text{Number of diagonals} = \frac{n(n-3)}{2} \]

where \( n \) is the number of sides. For a quadrilateral, \( n = 4 \):

\[ \text{Number of diagonals} = \frac{4(4-3)}{2} = \frac{4 \times 1}{2} = 2 \]

Thus, a quadrilateral has **2 diagonals**, not 4. Therefore, the assertion is **false**.

### Step 2: Analyze the Reason
The reason states: "A quadrilateral is a polygon made up of line segments."

- A quadrilateral is indeed a polygon.
- It consists of **4 line segments** (the sides of the quadrilateral).
- These line segments are typically labeled as AB, BC, CD, and DA.

Since this statement is true, we conclude that the reason is **true**.

### Conclusion
- The assertion is **false** because a quadrilateral has 4 angles but only 2 diagonals.
- The reason is **true** because a quadrilateral is indeed a polygon made up of 4 line segments.

### Final Answer
The assertion is false, and the reason is true.

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