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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)

Respuesta :

the internal angles of a regular pentagon add up to  540 degrrees so two of the angles add up to  2/5 * 540  = 216 degrees
so we multiply the given expression by 2/5  to get the answer.
(
(40x^2  - 65x  + 50)  * 2/5

= 16x^2 - 26x + 20)

= 2(8x^2 - 13x + 10)   which is choice B.

The expression that represents the measure of two angles is [tex]2\times (8x^2-13x+10)[/tex] and this can be determined by using the given data. The correct option is B).

Given :

Expression  --  [tex]40x^2-65x+50[/tex]

The following steps can be used in order to determine the expression that represents the measure of two angles:

  • Step 1 - The sum of interior angles of the pentagon is 540 degrees.

  • Step 2 - According to the given data, the expression [tex]40x^2-65x+50[/tex] represents the sum of the interior angles of a regular pentagon in degrees.

  • Step 3 - Let the two angles be [tex]\alpha[/tex] and [tex]\beta[/tex].

  • Step 4 - So, the sum of the two interior angles of the pentagon is:

                   [tex]\alpha +\beta =\dfrac{2}{5}\times (40x^2-65x+50)[/tex]

  • Step 5 - Further simplify the above expression.

             [tex]\alpha +\beta =2\times (8x^2-13x+10)[/tex]

So, the correct option is B).

For more information, refer to the link given below:

https://brainly.com/question/27476

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