Question

the ratio between an exterior angle and the interior angle is 1:5 find
measure of each exterior angle
measure of each interior angle
no. of sides in the polygon​

Answer 1

Answer:

x+5x=180°

6x=180°

x=30°

each of the angle are 30°and150°

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Answer 2

Step-by-step explanation:

Given that ratio between an exterior angle and the interior angle = 1:5.

We know that,

Measure of an interior angle = (n - 2)(180/n)

and,

The measure of an exterior angle = (360/n).

Therefore,

1/5. = (360/n) / (n-2)(180/n)

1/5. = (360/n) / n/(n-2)*180

1/5. = (360/n) / n(180n-360)

1/5. = (360) / (180 (n-2))

1/5. = 2 / ( n-2)

1(n-2) =5*2

n-2. = 10

n. = 12

Therefore number of sides of Polygon is 12

Therefore measure of each exterior angle. = (360/n)

= 360/12

= 30

And, measure of each interior angle. = 180-30

=150

HOPE THIS HELPS!!