the expression $40x^{2}-65x + 50$ represents the sum of the interior angles of a regular pentagon in…

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?\n$2x^{2}(20 - 32x+25x^{2})$\n$2(8x^{2}-13x + 10)$\n$5x^{2}(8x^{2}-13x + 10)$\n$5(3x^{2}-8x + 5)$

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?\n$2x^{2}(20 - 32x+25x^{2})$\n$2(8x^{2}-13x + 10)$\n$5x^{2}(8x^{2}-13x + 10)$\n$5(3x^{2}-8x + 5)$

Answer

Explanation:

Step1: Find measure of one angle

A regular pentagon has 5 equal - interior angles. The sum of the interior angles is (40x^{2}-65x + 50). So the measure of one angle is (\frac{40x^{2}-65x + 50}{5}). [ \begin{align*} \frac{40x^{2}-65x + 50}{5}&=\frac{40x^{2}}{5}-\frac{65x}{5}+\frac{50}{5}\ &=8x^{2}-13x + 10 \end{align*} ]

Step2: Find measure of two angles

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

Answer:

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