Question

The angles of a hexagon are x + 10°, 2x + 20°, 2x – 20°, 3x – 50°, x + 40° and x + 20°. Find x.

Answer 1

angles of a hexagon are x + 10°, 2x + 20°, 2x – 20°, 3x – 50°, x + 40° and x + 20°.

∴ But sum of angles of a hexagon = (x - 2) × 180°

= (6 - 2) × 180° = 4 × 180° = 720°

But sum = x + 10 + 2x + 20° + 2x - 20° + 3x - 50° + x + 40 + x + 20

= 10x + 90 - 70 = 10x + 20

∴ 10x + 20 = 720° 

⇒ 10x = 720 - 20 = 700

⇒ x = `700^circ/10 = 70^circ`

∴ x = 70°