Question

7. What is the ratio of the interior angles of a pentagon and a decagon?​

Answer 1

Answer:

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

Answer 2

The sum of the interior angles of the pentagon is 3 * 180. the sum of the interior angles of the decagon is 8 * 180. the ratio of the sum of the interior angles of a pentagon to the sum of the interior angles of a decagon is (3 * 180) / (8 * 180). this results in 3/8.