Question

What is the sum of the interior angles of an octagon?

a. 720°
b. 900°
c. 1080°
d. 1260°

Answer 1

Do you know the formula for finding the interior angles of a shape ?

Answer 2

look how many separate triangles you can make in an octagon

Answer 3

you can make 6 so 6*180 = angles in the octagon

Answer 4

you can always make 2 triangles less than the number of total points
for example 3 points
1 triangle
4 points - square has 2 triangles = 360 degrees
5 points - pentagon has 3 triangles = 3*180=540 degrees
6 points-hexdagon has 4 triangles = 4*180 = 720
and so on

Answer 5

8 points, octagon - 6 triangles = 6*180 = 600 + 80 * 6 = 600+480 = 1080

Answer 6

make sense?

Answer 7

Method 1
sum of interior angles of a polygon = (n – 2) × 180
in octagon number of sides n = 8
sum of interior angles = (8 – 2) × 180 = 1080

Method 2
sum of exterior angles of polygon is always 360°
and each exterior angle = 360/n = 360/8 = 45°
so so each interior angle = 180 – 45 = 135°
so sum of 8 interior angles = 8 × 135 = 1080°

Answer 8

Thank you!