Question

What is the sum of all the angles of a pentagon?

• A. $180°$
• B. $360°$
• C. $540°$
• D. $720°$

Answer 1

The correct option is C

$540°$

Determine the sum of all the angles of a pentagon.

The sum of all the interior angles of a simple $n-\mathrm{gon}$is$(n-2)\times 180°$ Or $\mathrm{Sum}=(n-2)\mathrm{\pi }\mathrm{radians}$.

Where $\text{'}n\text{'}$ is the number of sides of a polygon Pentagon has 5 sides, so$n=5$

Calculate the sum of all the angles of a pentagon:

$$\begin{gathered} \mathrm{Sum}=(\mathrm{n}–2)\times 180° \\ \Rightarrow \mathrm{Sum}=(5–2)\times 180° \\ \Rightarrow \mathrm{Sum}=3\times 180° \\ \Rightarrow \mathrm{Sum}=540° \end{gathered}$$

Hence, the sum of all the angles of a pentagon is $540°$.