Angles of Triangles and Polygons

10.3a Polygons and Angles

Finite Math

EQ: Tuesday, November 7, 2023

• How do I name polygons?

• What are the measures of the interior and exterior angles of polygons?

What are Polygons?

Any closed shape in a plane formed by 3 or more lines segments.

​Polygons

​Sides Name

​3 Triangle
4 Quadrilateral
5 Pentagon
6 Hexagon
7 Heptagon
8 Octagon
9+ 9-gon (etc)

Match

Match the Name with the Number of Sides

• 3 Sides

• 4 Sides

• 5 Sides

• 6 Sides

• 8 Sides

Triangle

Quadrilateral

Pentagon

Hexagon

Octagon

• Triangle

• Quadrilateral

• Pentagon

• Hexagon

• Octagon

Equilateral (or Regular) Polygons

Congruent Sides and Congruent Angles

Equilateral Triangle:

Equilateral Quadrilateral:

The sum of the interior angles in a triangle is 180°.

Multiple Choice

Cutting from vertex to vertex, how many triangles make up this hexagon (6-sided polygon)?

• 4

• 5

• 6

• 7

• 3

​6 Sides = 4 Triangles = 4 x 180 = 720

Multiple Choice

Cutting from vertex to vertex, how many triangles make up this Octagon (8-sided polygon)?

• 3

• 4

• 5

• 6

• 7

​6 Sides = 4 Triangles = 4 x 180 = 720








8 Sides = 6 Triangles = 6 x 180 = 1080

​The sum of the interior angles of a polygon is

Multiple Choice

Find the missing angle.

• $$150\degree$$

• $$180\degree$$

• $$140\degree$$

• $$95\degree$$

6 Sides => Sum of angles = 180(6 - 2) = 720

720 – (40 + 160 + 120 + 100 + 150) = 150

What is the measure of the missing angle?

Multiple Choice

Find the measure of EACH angle in a REGULAR heptagon.

• $$128.6\degree$$

• $$150\degree$$

• $$100\degree$$

• $$175\degree$$

Find the measure of each angle in a regular heptagon (7 sides).

Sum of angles in a heptagon

S = 180(7 – 2) = 900

900 ÷ 7 ≈ 128.6o

128.6

​Exterior Angles of Polygons

​measured as the angle from the extended side of the interior angle

supplementary to the interior angle

Multiple Choice

Find the measure of one exterior angle in a REGULAR heptagon.

• $$51.4\degree$$

• $$128.6\degree$$

• $$100\degree$$

• $$60\degree$$

128.6°

51.4°
Exterior

Multiple Choice

Find the measure of ONE of the interior angles of the regular polygon.

• $$144\degree$$

• $$120\degree$$

• $$140\degree$$

• $$180\degree$$

Multiple Choice

Find the measure of one exterior angle in the REGULAR polygon.

• $$36\degree$$

• $$44\degree$$

• $$88\degree$$

• $$144\degree$$

• ​Finding the sum of the interior angles of a polygon.

• Finding the measure of each interior angle in a regular polygon.

• Finding the measure of each exterior angle of a regular polygon.

• Finding the sum of the exterior angles in any polygon.

​Notes