Question

What is the sum of the interior angles of a octagon

Answer 1

Sum of Interior Angles = (n-2) × 180°
where n is the number of sides
Here it is 8 ..So
Answer = (8-2) x 180°
= 6 x 180°
= 1080°

Answer 2

\(\Large \color{red}{Method\ 1} \)
sum of interior angles of a polygon \(\Large = (n – 2) × 180 \)
in octagon number of sides \(\Large n = 8 \)
sum of interior angles \(\Large = (8 – 2) × 180 = 1080\)

\(\Large \color{red}{Method\ 2}\)
sum of exterior angles of polygon is always \(\Large 360°\)
and each exterior angle \(\Large = 360/n = 360/8 = 45° \)
so so each interior angle \(\Large = 180 – 45 = 135° \)
so sum of 8 interior angles \(\Large = 8 × 135 = 1080° \)