Question

show that an exterior angle of a regular convex octagon is one third of its interior angle

Answer 1

$\bold{\text{sum of interior and exterior angles are}180^{\circ}}$

According to question,
Exterior angle is one third of interior angle
Let exterior angle is x
Then, interior angle be 3x

now, x + 3x = 180°
⇒ 4x = 180°
x = 180°/4 ⇒ 45°

now, use formula,
Number of sides = 360°/exterior angle = 360°/45° = 8

Hence, number of sides = 8 so, it is convex octagon