Fix the mistake: Calculating Angles
Angle Calculations ① Interior and Exterior Angles of Triangles and Polygons
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.
Previous and next lessons in this course
- Previous lesson: Math Test Grade 6 quiz
- Next lesson: Fix the mistake: Calculating Angles