Question

The ratio between an exterior angle and the interior angle of a regular polygon is 1:5. find (i) the measure of each exterior angle . (ii) the measure of each interior angle . (iii) the number of sides in the polygon.

Answer 1

Answer:

Measurement of each

1) Exterior angle= 20°

2) Interior Angle= 100°

3) Number is sides =18

Step-by-step explanation:

(i) Let the ratio of angles be 1x:5x

1x+5x=120°( Linear pair)

6x= 120°

x= 120÷6

x= 20°

Ans. Each Exterior angle= 1x=1×20=20°

ii) Each interior angle= 5x=5×20=100°

iii) No of sides= 360°÷ each exterior angle

360°÷20=18 sides( Ans.)

Answer 2

Step-by-step explanation:

let the ratio be 1x and 5x

therefore 1x+5x=180

6x=180

x=30

the formula to find no of sides of polygon is 360÷each exterior angle i.e

360÷30=12

the no of sides is 12 its a 12 sided polygon

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