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A convex pentagon has the following measurements for its interior angles: (x-8), (3x-11), (x+8), (x), and (2x+7). Which of the following could be measurements for interior angles of the pentagon? Select all that apply.



A: 60


B: 68


C: 76


D: 108


E: 193


F: 540

Respuesta :

tramserran

Answer: A, B, C, E

Explanation:

The sum of the interior angles of a polygon can be determined by the formula: (n - 2)180 ; where n represents the number of sides.  Since a pentagon has 5 sides, then (5 - 2)180 = 540

 x - 8

3x - 11

 x + 8

 x

2x + 7

8x - 4  =  540

    +4        +4

8x        =  544

÷8            ÷8  

 x         =   68

**********************

x - 8    ⇒     68 - 8 = 60  (A)

3x - 11   ⇒     3(68) - 11 = 193 (E)

 x + 8   ⇒     (68) + 8 = 76 (C)

 x         ⇒     (68)  (B)

2x + 7   ⇒     2(68) + 7 = 143

The sumof the pentagon's interior angles is: 540°

According to the Question, we have: (x-8)+(3x-1)+(x+8)+x+(2x+7)=540

x-8+3x-11+x+8+x+2x+7=540

x+3x+x+x+2x=540+8+11-8-7

8x=544

x=544/8=68


(x-8)=68-8=60 (choose letter A)

(3x-11)=3*68-11=193 (choose letter E)

(x+8)=68+8=76 (choose letter C)

(x)=68 (choose letter B)

(2x+7)=2*68+7=143 (cannot select any letter)

In short, we choose letter A, B, C and E.

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