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

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

Answer:

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