Question

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

Answer 1

each interior angle of Pentagon=(2*5-4)*90/5
=(10-4)*18
=6*18
=108

each interior angle of decagon =(2*10-4)*90/10
=(20-4)*9
=16*9
=144

the ratio=108/144
=9/12
=3/4

Answer 2

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°

STEP 2: Find one interior angle:

one interior angle = 540 ÷ 5 = 108

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°

STEP 4: Find one interior angle:

one interior angle = 1440 ÷ 10 = 144

STEP 5: Find the ratio:

Pentagon : Decagon = 108 : 144

Simplify:

Pentagon : Decagon = 3:4

Answer: The ratio is 3 : 4