Question

Two angles of a hexagon are 120° and 160°. If the remaining four angles are equal, find each equal angle.

Answer 1

Two angles of a hexagon are 120°, 160°

Let the remaining four angles be x, x, x and x.

Their sum = 4x + 280°

But the sum of all the interior angles of a hexagon

= (6 - 2) × 180°

= 4 × 180° = 720°

∴ 4x + 280° = 720°

⇒ 4x = 720° - 280° = 440°

⇒ x = 110°

∴ Equal angles are 110° (each)