Question

Find the measure of each interior angle and each exterior angles of the following regular polygons. Show your work. Decagon Pentagon Dodecagon 16-gon 25-gon

Answer 1

Hey there,
Decagon -
(10 - 2) x 180 degrees
= 8 x 180 degrees
= 1,440 degrees (sum of angles)
1 angle = 1,440 degrees / 10
= 144 degrees
Pentagon -
(5 - 2) 180 degrees = 3 x 180 degrees
= 540 degrees (sum of angles)
1 angle = 540 degrees / 5
= 108 degrees
Do decagon -
(12 - 2 ) x 180 degrees = 10 x 180 degrees
= 1,800 degrees (sum of angles)
1 angle = 1,800 / 12
= 150 degrees
16 - gon -
( 16 - 2) x 180 degrees = 14 x 180 degrees
= 2,520 degrees (Sum of angles)
1 angle = 2,520 degrees / 16
= 157.5 degrees
25 - gon -
(25 - 2) x 180 degrees = 23 x 180 degrees
= 4,140 degrees (sum of angles)
1 angle = 4,140 / 25
= 165.6 degrees
The formula = (n - 2) x 180 degrees

Hope this helps :))

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