Question

2 exterior angles in an irregular polygon are 72 and 108 while all remaining exterior angles are equal to 45. Find the number of sides of the polygon and deduce it's name. ​

Answer 1

It has 10 sides and its name is Decagon

Explanation:

∵ The measure of the rest of all exterior angles in the polygon are 45°

∵ The measure the interior angle + its exterior angle = 180°

∴ The the measures of their interior angles also = 180° - 45° = 135°

∵ The measure of all interior angles are equal except 2 angles

∴ We can find the number of the sides of the equal angles and then add 2

∵ The rule to find the measure of an angle a polygon if they are equal is:

`(n-2)/(n)(180)=` measure of an angle

∵
`((n-2)180)/(n)=135`⇒ n is the number of sides (angles)

∴ 180n - 360 = 135n⇒ collect like terms

∴ 180n - 135n = 360

∴ 45n = 360

∴ n = 360/45 = 8

∴ The number of sides (angles) of the irregular polygon = 8 + 2 = 10 sides

∴ Its name is Decagon