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?
2x²(20 - 32x + 25x²)
2(8x² - 13x + 10)
5x²(8x² - 13x + 10)
5(3x² - 8x + 5)

Explanation:

Step1: Find measure of one angle

A regular pentagon has 5 equal - interior angles. If the sum of the interior angles is \(40x^{2}-65x + 50\), then 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

To find the measure of two angles, we multiply the measure of one angle by 2. So, \(2\times(8x^{2}-13x + 10)=2(8x^{2}-13x + 10)\)

Answer:

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