We will find angles using the rules for the sums of the interior angles and exterior angles of polygons (triangles, quadrilaterals, pentagons, and so on).
Rules to Remember
- Sum of the interior angles of an n-gon = 180° × (n − 2)
- The sum of the exterior angles of any polygon is always 360°.
- One exterior angle of a triangle = the sum of the two nonadjacent interior angles
Example 1: What is the sum of the interior angles of a pentagon?
Solution: 180 × (5 − 2) = 180 × 3 = 540°
Solution: 180 × (5 − 2) = 180 × 3 = 540°
Example 2: Two interior angles of a triangle are 65° and 75°. Find the remaining interior angle and its exterior angle.
Solution:
① Interior angle → 180 − 65 − 75 = 40°
② Exterior angle → sum of the two nonadjacent interior angles = 65 + 75 = 140°
Solution:
① Interior angle → 180 − 65 − 75 = 40°
② Exterior angle → sum of the two nonadjacent interior angles = 65 + 75 = 140°
An n-gon can be divided into (n − 2) triangles by drawing lines from one vertex. Thinking this way helps us understand the formula for the sum of the interior angles.