Aptitude Discussion

Q. |
How many diagonals can be drawn in a pentagon? |

✔ A. |
5 |

✖ B. |
7 |

✖ C. |
8 |

✖ D. |
10 |

**Solution:**

Option(**A**) is correct

A pentagon has $5$ sides. We obtain the diagonals by joining the vertices in pairs.

Total number of sides and diagonals:

$= {^5C_2}$

$= \dfrac{5×4}{2×1}$

$= 5×2$

$= 10$

This includes its $5$ sides also.

⇒ Diagonals $= 10 - 5 = 5$

Hence the number of diagonals,

$= 10 - 5$

$= 5$

**Raj Singh**

*()
*

From one vertex, you can draw 3 diagonals. From second vertex again you can draw 3 more diagonals. From third vertex again you can draw 3 more diagonals. Overall, you can draw 5x3=15 diagonals in a pentagon.