Question

125
(6)
2. Find the measure of each exterior angle of a regular polygon of
How many sides does a regular polygon have if the measure of an ext
ular nolygon have if each of its
@ 15 sides
1 9 sides
2​

Answer 1

We are asked to solve,

${\large{\pmb{\sf{\underline{Correct \: question...}}}}}$

⋆ Find the measure of each exterior angle of a regular polygon of

• 15 sides and 9 sides

${\bigstar \:{\pmb{\sf{\underline{Provided \: that...}}}}}$

a. Side of regular polygon is 15 sides

b. Side of regular polygon is 9 sides

• Find the measure of each exterior angle of regular polygon.

${\bigstar \:{\pmb{\sf{\underline{Solution...}}}}}$

a. Side of regular polygon is 15 sides

• Measure(exterior angle) = 24°

b. Side of regular polygon is 9 sides

• Measure(exterior angle) = 40°

${\bigstar \:{\pmb{\sf{\underline{Knowledge \: required...}}}}}$

⋆ The sum of the measure of the external angles of any polygon is 360 degree.

⋆ We can say that the exterior angles have equal measure.

${\bigstar \:{\pmb{\sf{\underline{Assumption...}}}}}$

⋆ As the exterior angles have equal measure, we can say it as x

${\large{\pmb{\sf{\underline{Required \: Solution...}}}}}$

${\bigstar \:{\pmb{\sf{\underline{Solution \: first...}}}}}$

⇒ Given sides 15

⇒ The sum of the measure of the external angles of any polygon is 360 degree.

⇒ 15x = 360°

⇒ x = 360/15

⇒ x = 24 degree

⇒ External angle = 24 degree

${\bigstar \:{\pmb{\sf{\underline{Solution \: second...}}}}}$

⇒ Given sides 9

⇒ The sum of the measure of the external angles of any polygon is 360 degree.

⇒ 9x = 360°

⇒ x = 360/9

⇒ x = 40 degree

⇒ External angle = 40 degree

Answer 2

Answer:

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Step-by-step explanation:

★ Solution first...

⇒ Given sides 15

⇒ The sum of the measure of the external angles of any polygon is 360 degree.

⇒ 15x = 360°

⇒ x = 360/15

⇒ x = 24 degree

⇒ External angle = 24 degree

★ Solution second...

⇒ Given sides 9

⇒ The sum of the measure of the external angles of any polygon is 360 degree.

⇒ 9x = 360°

⇒ x = 360/9

⇒ x = 40 degree

⇒ External angle = 40 degree