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Given the following angles of a regular polygon, 120°, (4*x+-3)°, (x+14)°, 45°, 135°, (x-31)°, and (x*6+20)°, what is the value of x?

User Vishal Panara
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1 Answer

22 votes
22 votes

Since the polygon has seven angles we deduce it is a heptagon. In that case the sum of the interior angles must be equal to 900°. We can formulate the following equation accordingly.

120°+(4*x-3)°+ (x+14)°+ 45°+ 135°+ (x-31)°+ (x*6+20)° = 900°

120°- 3° +14° + 45° + 135° - 31° + 20 + 4x + x + x + 6x = 900° (Organizing)

300 ° + 12x = 900° (Operating like terms)

12x= 900° - 300° (Transposing 300° to the other side of the equation)

12x= 600° (Subtracting 300° from 900°)

12/12x= 600° / 12 (Dividing by 12 on both sides of the equation)

x= 50°

Answer is: x= 50°

User Ankit Mishra
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