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Given the convex pentagon in the image, what is the value of x? All angle measures are in degrees.

Given the convex pentagon in the image, what is the value of x? All angle measures-example-1
User Alan Le
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1 Answer

6 votes

Answer:

x = 20°

Explanation:

  • Find the sum of angles of pentagon.

Sum of all angles of n-sided polygon = 180*(n-2)

n = number of sides = 5

Sum of all angles of pentagon = 180 * 3

= 540°

  • ∠A + ∠B + ∠C + ∠D + ∠E = 540

5x + 2 + 3x + 5 + 8x + 8 + 4x + 15 + 5x + 10 = 540

  • Combine the like terms,

5x + 3x + 8x + 4x+ 5x + 2 + 5 + 8 + 15 + 10 = 540

25x + 40 = 540

  • Subtract 40 from both sides,

25x = 540 - 40

25x = 500

  • Divide both sides by 25,


\sf x = (500)/(25)\\\\\\\boxed{\bf x = 20^\circ}

Answer: x = 20°

User Newbyman
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