Find the measure of each interior angle and each exterior angle of the following regular polygons. show your work

Step-by-step explanation:

As we know for a regular polygon sum of all interior angles is represented by  n A = 180 (n-2)

and sum of all exterior angles is represented by n A' = 360°

Here n represents number of sides of the polygon.

Now we will go for each options given.

(A) Decagon : (Having 10 sides)

(1) 8A = 180 ( 8-2 )

  8A  = 180 × 6

  A = = 160°  ( interior angle )

(2) n A' = 360°

  8 A' = 360°

  A = 45°     ( exterior angle )

(B) Pentagon ( having 5 sides )

(1) 5A = 180 ( 5-2 )

   5A = 180 × 3 = 540

   A = 108°   ( interior angle )

(2) 5A' = 360

    A' = 72°    (exterior angle )

(C) Dodecagon : ( having 12 sides )

(1)   12A  = 180 (12-2)

    12 A = 180 × 10 = 1800

     A = 150°  ( interior angle )

(2) 12 A' = 360

    A' = 30°   ( exterior angle )

(D) 16-gon  ( having 16 sides )

(1)   16 A = 180 ( 16 - 2 )

   16A = 180 × 14

  16 A  = 1520

  A  = 157.5°    ( interior angle )

(2)  16 A'  = 360

    A' = 22.5°

(E)  25-gon   ( having 25 sides )

(1)   25 A = 180 ( 25-2)

    25A = 180  (23)

    A = 165.6°     ( interior angle )

(2)  25A'  =  360

  A  = 14.4°    ( exterior angle)

70

step-by-step explanation:

2*5=10

4*15=60

60+10=

70

56.6

step-by-step explanation:

the ratio of the perimeters is equal to the scale.

the ratio of the areas is equal to the square of the scale.

34 / 20 = k

a / 19.6 = k²

substituting:

a / 19.6 = (34 / 20)²

a = 19.6 (34 / 20)²

a ≈ 56.6