Question

1. practice: summarizing

fill in the blanks to explain the formula.
sum of interior angles formula
sum = (n - 2)180°
sum = sum of interior angles in any polygon
n = polygons number of sides
(n - 2) = number of triangles in polygon
180° = sum of interior angles in a triangle

1. practice: organizing information

complete the chart.

polygon	number of sides	number of triangles	sum of interior angles
quadrilateral	4		360°

Explanation:

Step1: Recall polygon - triangle relation

Diagonals of a polygon divide it into triangles. For a polygon with \(n\) sides, the number of triangles formed is \(n - 2\).

Step2: Use the sum of interior - angles of a triangle

The sum of the interior angles of a triangle is \(180^{\circ}\). To find the sum of the interior angles of a polygon, we multiply the number of triangles (\(n - 2\)) by \(180^{\circ}\).

Step3: Fill in the quadrilateral values

For a quadrilateral (\(n=4\)), the number of triangles is \(n - 2=4 - 2 = 2\). The sum of the interior angles is \((n - 2)\times180^{\circ}=(4 - 2)\times180^{\circ}=360^{\circ}\).

Answer:

Polygon	Number of sides	Number of triangles	Sum of interior angles
quadrilateral	4	2	\(360^{\circ}\)