Question

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

Answer 1

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°