Question

What is the ratio of the interior angles of a pentagon and decagon

Answer 1

$\textbf {Hey there, here is the solution.}$

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STEP 1: Find the sum of the interior angles of a pentagon

A pentagon has 5 sides.

Sum of the interior angles = ( n - 2) x 180

Sum of the interior angles = ( 5 - 2) x 180

Sum of the interior angles = 540°

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STEP 2: Find one interior angle:

one interior angle = 540 ÷ 5 = 108°

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STEP 3: Find the sum of interior angles of a decagon

A decagon has 10 sides

Sum of the interior angles = ( n - 2) x 180

Sum of the interior angles = ( 10 - 2) x 180

Sum of the interior angles = 1440°

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STEP 4: Find one interior angle:

one interior angle = 1440 ÷ 10 = 144°

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STEP 5: Find the ratio:

Pentagon : Decagon = 108 : 144

Simplify:

Pentagon : Decagon = 3 : 4

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Answer: The ratio is 3 : 4

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⭐$\textbf {Cheers}$⭐

Answer 2

Answer:

each interior angle of Pentagon=(2*5-4)*90/5

=(10-4)*18

=6*18 =108

each interior angle of decagon =12*10-4)*90/10

=(20-4)*9

=1699

=144

the ratio=108/144 =9/12

=3/4

hope it helps you

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