Question

Q 12 please ............

Answer 1

Given:  Ratio of sides of '2 regular' polygons = 5:4

Let us assume the sides be 5X , 4X

Given: Interior angle difference = 6 degrees.

Formulas:

Interior angle = 180 - Exterior angle

Exterior angle of a regular polygon = 360/Number of sides

Exterior angle of 1st polygon = 360/5X .......... (a)

Exterior angle of 2nd polygon = 360/4X ....... (b)

So, Interior angle of 1st polygon = 180 - 360/5X .......(c)

Interior angle of 2nd polygon = 180 - 360/4X .......(d)

Interior angle difference = 6 degrees

180 - 360/5X - [180 - 360/4X] = 6

180 - 360/5X - 180 + 360/4X = 6

-360/5X + 360/4X = 6        [180-180 cancels each other]

360 [ 1/4X - 1/5X ] = 6

360 [ 5/20X - 4/20X ] = 6         [Taking LCM of denominator(4,5)==20]

360*1/20X = 6

360/20*6 = X

360/120 = X

Hence, X = 3

Now sides ratio were- 5X:4X

Sides = 5*3 : 4*3 = 15, 12

Hence sides of regular polygons = 15,12

Hope it helps.