Question

And exterior angle of a regular polygon is 36 degrees and one of its longest diagonal is 10 centimetres then find its perimeter

Answer 1

Sum of all exterior angles in a polygon is 360º

Find the number of sides:

One exterior angle = 36º

Total number of sides = 360 ÷ 36 = 10

⇒ It is a 10 sided polygon

Find one interior angle:

exterior angle + Interior angle = 180

36 + interior angle = 180

interior angle = 180 - 36 = 144º

See attachment:

Find ∠ABD:

∠ABC = Interior angle = 144º

∠ABD = 144 ÷ 2 = 72º

Find ∠BAD:

∠BAD = 72º (isosceles triangle)

Find ∠ADB:

∠ ADB = 180 - 72 - 72 (Sum of triangle = 180º)

∠ ADB = 36º

Find length AD:

Diagonal = 10 cm

Length AD = 10 ÷ 2 = 5 cm

Find length AB:

a/sin A = b/sin B

5/sin(72) = AB/sin(36)

AB sin (72) = 5 sin (36)

AB = 5 sin (36) ÷ sin (72)

AB = 3.09 cm

Find the perimeter:

There are 10 sides

Each side is 3.09 cm

Perimeter = 3.09 x 10 = 30.9 cm

Answer: Perimeter = 30.9 cm

Answer 2

Answer:

The sum of all Interior angles of a polygon which having 49/7 sides is equal to