Question

the expression $40x^2 - 65x + 50$ 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?
$2x^2(20 - 32x + 25x^2)$
$2(8x^2 - 13x + 10)$
$5x^2(8x^2 - 13x + 10)$
$5(3x^2 - 8x + 5)$

Explanation:

Step1: Find measure of one angle

A regular pentagon has 5 equal interior angles. So, measure of one angle is $\frac{40x^2 - 65x + 50}{5}$. Simplify this: divide each term by 5. $40x^2\div5 = 8x^2$, $-65x\div5=-13x$, $50\div5 = 10$. So one angle is $8x^2-13x + 10$.

Step2: Find measure of two angles

Multiply the measure of one angle by 2. So two angles: $2(8x^2-13x + 10)$.

Answer:

B. $2(8x^2 - 13x + 10)$