Question

The sum of the measures of the interior angles of a convex regular polygon is 3960°. What is the polygon by the number of sides. What is measure of each interior angle?

Answer 1

`165^circ`

Explanation:

Always remember the formula (very important in geometry)

Let the number of sides of a polygon (convex) `=n`

Then the sum of measures of angles `=color(blue)((n-2)*180`

`:.` Substitute the formula

`color(purple)(rarr(n-2)*180=3960`

Divide both sides by `180`

`color(purple)(rarr((n-2)*cancel180)/cancel180=3960/180`

`color(purple)(rarr(n-2)=22`

Remove the brackets

`color(purple)(rarrn-2=22`

Add `2` both sides

`color(purple)(rArrn=24`

`:.` the number of sides of the polygon is `24`

So,

Each interior angle=Sum of measure of all angles / number of sides

`rarr3960/24`

`color(green)(rArr165^circ`