Question

Find the measure of each exterior angle of a regular polygon of
(i) 10 sides (ii) 15 sides

Answer 1

Answer:

(i) 36° (ii) 24°

Step-by-step explanation:

Measure of exterior angle of n-sided polygon = 360/n

Therefore,

Exterior angle of a 10-sided polygon = 360/10 = 36°

Exterior angle of a 15-sided polygon = 360/15 = 24°

Answer 2

Answer:

i) We all know that sum of all the angles of 10sided polygon is 360° if you don't so it is a rule

now in the question it is given that the polygon is 10 sided so all the side would be equal as

it is a regular polygon

now let us give it a name as "x"

So,

10x=360

x=360÷10

x=36

so each angle measure is 36°

ii) 15 sides

For a n-sided regular polygon, sum of internal angles = (n-2)×180°

Since all internal angles are equal, the internal angle can is given as:

Here, it is given that the polygon has 15 sides.

So n = 15

So each internal angle is 156°.

Internal and external angle are always supplementary. So sum of the internal and external angle is 180°.

So external angle = 180° - 156° = 24°.

Measure of each external angle is 24°.

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