Answer:
The value of x is 27
Step-by-step explanation:
The sum of the exterior angles of the n-side polygon is 360°
Let us use this rule to solve the question
∵ The given polygon has 4 sides
∴ It has 4 exterior angles, one on each vertex
→ By using the rule above
∴ The sum of the 4 angles is 360°
∵ The exterior angles are (2x + 40)°, (4x)°, (x + 50)°, and (3x)°
→ Add them, then equate the sum by 360
∴ (2x + 40) + (4x) + (x + 50) + 3x = 360
→ Add the like terms in the left side
∵ (2x + 4x + x + 3x) + (40 + 50) = 360
∴ 10x + 90 = 360
→ Subtract 90 from both sides
∵ 10x + 90 - 90 = 360 - 90
∴ 10x = 270
→ Divide both sides by 10
∴ x = 27
∴ The value of x is 27
