Question

additional example 1
find the sum of the interior angles of the polygon.
solution

Explanation:

Step1: Identify the polygon type

The figure is a quadrilateral (a rectangle, which is a type of quadrilateral). For a polygon with \( n \) sides, the formula for the sum of interior angles is \( S=(n - 2)\times180^{\circ} \). For a quadrilateral, \( n = 4 \).

Step2: Apply the formula

Substitute \( n = 4 \) into the formula \( S=(n - 2)\times180^{\circ} \).
\[

$$\begin{align*} S&=(4 - 2)\times180^{\circ}\\ &=2\times180^{\circ}\\ &= 360^{\circ} \end{align*}$$

\]

Answer:

The sum of the interior angles of the polygon (quadrilateral) is \( 360^{\circ} \)