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 the measure of one angle

Since the sum of interior angles of a regular pentagon is \(40x^{2}-65x + 50\) and a pentagon has \(5\) equal interior angles.
The measure of one angle is \(\frac{40x^{2}-65x + 50}{5}\).
Using the distributive property \(\frac{a + b + c}{d}=\frac{a}{d}+\frac{b}{d}+\frac{c}{d}\), we have \(\frac{40x^{2}}{5}-\frac{65x}{5}+\frac{50}{5}=8x^{2}-13x + 10\).

Step2: Find the measure of two angles

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

Answer:

\(2(8x^{2}-13x + 10)\) (the second option)