Question

The expression 40x2 – 65x + 50 represents the sum of the interior angles of a regular pentagon in degrees. If the interior angles of the pentagon are equal, which expression represents the measure of two angles?

Answer 1

there are 5 interior angles so each angle =

(40x^2 - 65x + 50) / 5 = 8x^2 - 13x + 10

so for 2 angles it's 16x^2 - 26x + 20 Answer

Answer 2

Expression representing the measure of the two angles of the given regular polygon is 16x² - 26x + 20.

Explanation:

Given Expression of the Sum of the all interior angles of a regular polygon

40x² - 65x + 50

We need to find expression representing the measure of the two angles.

We know that regular polygons have all side and all angles equal.

Number of side or angles in regular polygon = 5

So, when we divide given expression by 5 we get expression for an angle of the regular polygon.

`(40x^2-65x+50)/(5)=(5(8x^2-13x+10))/(5)=8x^2-13x+10`

Expression for an angle of regular pentagon = 8x² - 13x + 10

Now, For 2 angles = 2( 8x² - 13x + 10 ) = 16x² - 26x + 20

Therefore, Expression representing the measure of the two angles of the given regular polygon is 16x² - 26x + 20.