Question

the angles of a heptagon are (x+3)°,(2x+5)°,(x+8)°,(3x+1)°,(5x-6)°,(2x+9)°and(x-5)°.calculate x

Answer 1

total angle = 900°
then adding all = 900°
15x + 15 = 900°
x+1 = 900/15
x+1 = 60
x = 59

Answer 2

Hey Mate,

As we all know a heptagon has 7 sides. Hence, it also has 7 angles.

We also know that sum of interior angles of a polygon is equal to 360°.

Then,

=> (x+3)° + (2x+5)° + (x+8)° + (3x+1)° + (5x-6)° + (2x+9)° + (x-5)° = 360°

On breaking the brackets, we get:-

=> x + 3 + 2x + 5 + x + 8 + 3x + 1 + 5x - 6 + 2x + 9 + x - 5 = 360°

On transposing, all constants from LHS to RHS, we get:-

=> x + 2x + x + 3x + 5x + 2x + x = 360 - 3 - 5 - 8 - 1 + 6 - 9 + 5

=> 15x = 345

On transposing 15 from LHS to RHS, we get:-

=> x = 345/15

=> x = 23

Therefore, x = 23

Hope it Helps!