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

`16x^2-26x+20`

Explanation:

Since it represents the sum of interior angles, the angle is essentially:
`angle + angle + angle + angle + angle`, and there are 5 angles since a pentagon has 5 interior angles. To find what one interior angle is, we simply divide the polynomial by 5, to do this we can just divide each coefficient by 5 (distributing the division):
`(40x^2-65x+50)/(5) = (40x^2)/(5) - (65x)/(5) + (50)/(5)` this simplifies to:
`8x^2-13x+10`. This represents what one of the interior angles is. Since we want an expression measuring two of the angles, we simply multiply this polynomial by 2, to do this we just multiply each coefficient by 2 (distributing the 2):
`2(8x^2-13x+10) = 16x^2-26x+20` which is the solution