Question

Find the measure of an exterior angle of a regular pentagon and an exterior angle of a regular
decagon. What is the ratio between these two angles?​

Answer 1

The measure of an exterior angle of a regular pentagon is 72 degrees

The measure of an exterior angle of a decagon is 36 degrees

Solution:

Find the measure of an exterior angle of a regular pentagon

Pentagon has 5 sides

The sum of the exterior angles of any polygon is always 360 degrees

Therefore,

$Each\ Exterior\ angle\ of\ pentagon = \frac{360}{5} = 72^{\circ}$

Find the measure of an exterior angle of a decagon

Decagon has 10 sides

Therefore,

$Each\ Exterior\ angle\ of\ decagon = \frac{360}{10} = 36^{\circ}$

What is the ratio between these two angles?​

Ratio = 72 : 36

Reduce to lowest form

Ratio = 2 : 1

Thus ratio between these two angles is 2 : 1

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Answer 2

Answer:

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Step-by-step explanation:

pentagon is 72 degrees

The measure of an exterior angle of a decagon is 36 degrees

Solution:

Find the measure of an exterior angle of a regular pentagon

Pentagon has 5 sides

The sum of the exterior angles of any polygon is always 360 degrees

Therefore,

Each\ Exterior\ angle\ of\ pentagon = \frac{360}{5} = 72^{\circ}Each Exterior angle of pentagon=

5

360

=72

∘

Find the measure of an exterior angle of a decagon

Decagon has 10 sides

Therefore,

Each\ Exterior\ angle\ of\ decagon = \frac{360}{10} = 36^{\circ}Each Exterior angle of decagon=

10

360

=36

∘

What is the ratio between these two angles?

Ratio = 72 : 36

Reduce to lowest form

Ratio = 2 : 1

THANK YOU...

Thus ratio between these two angles is 2 : 1