Find the interior angle for each regular polygon. Round the answer to nearest te...

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September 2022 1 7 Report

Find the interior angle for each regular polygon. Round the answer to nearest tenths if necessary.

1-3.

Sum of the interior angles -
Each interior angle -

Answers & Comments

NayeonMyBabyBunny

$\pink{••••••••••••••••••••••••••••••••••••••••••••••••••}$

$\large\boxed{\rm\purple{ANSWER :}}$

» $\sf{Number\:1.}$

Sum of the interior angles - 1 080°
Each interior angle - 135°

» $\sf{Number\:2.}$

Sum of the interior angles - 360°
Each interior angle - 90°

» $\sf{Number\:3.}$

Sum of the interior angles - 1 440°
Each interior angle - 144°

$\pink{••••••••••••••••••••••••••••••••••••••••••••••••••}$

$\large\boxed{\rm\purple{SOLUTION :}}$

To find the sum of the measure of the interior angles and the measure of each interior angle of a regular polygon, use the formulas below.

Sum of the interior angles:

$\sf{(n - 2) × 180°}$

Each interior angle:

$\large{ \sf \frac{S}{n}}$

- Note that n represents the number of sides and S represents the sum of the interior angles of the regular polygon on the formulas.

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» $\sf{Number\:1.}$

Sum of the interior angles:

$\sf{(n - 2) × 180°}$

$\sf{(8 - 2) × 180°}$

$\sf{6 × 180°}$

$\green{ \sf{1\:080°}}$

Each interior angle:

$\large{ \sf \frac{S}{n}}$

$\large{ \sf \frac{1\:080°}{8}}$

$\green{ \sf{135°}}$

» $\sf{Number\:2.}$

Sum of the interior angles:

$\sf{(n - 2) × 180°}$

$\sf{(4 - 2) × 180°}$

$\sf{2 × 180°}$

$\green{ \sf{360°}}$

Each interior angle:

$\large{ \sf \frac{S}{n}}$

$\large{ \sf \frac{360°}{4}}$

$\green{ \sf{90°}}$

» $\sf{Number\:3.}$

Sum of the interior angles:

$\sf{(n - 2) × 180°}$

$\sf{(10 - 2) × 180°}$

$\sf{8 × 180°}$

$\green{ \sf{1\:440°}}$

Each interior angle:

$\large{ \sf \frac{S}{n}}$

$\large{ \sf \frac{1\:440°}{10}}$

$\green{ \sf{144°}}$

$\pink{••••••••••••••••••••••••••••••••••••••••••••••••••}$

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