Question

plz solve it with steps

Answer 1

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The formula for angle sum in any n-gon is Sum=(n-2)*180.

In a regular n-gon, each angle will be the average, or the sum divided by n:

(n-2)*180/n

Given: (n-2)*180/n = 145

Multiply by n: (n-2)*180 = 145n

Distribute: 180n - 360 = 145n

Subtract 145n: 35n - 360 = 0

Divide by 35: n - 12 = 0.

Add 12: n = 12.

So a regular 12-sided polygon (a regular dodecagon) has 120 degree interior angles.