Question

four interior angles of a hexagon are 114degree,130degree,140degree and 96degree. Find the size of each of the remaining two angles, if one of them is three times the other​

Answer 1

60° and 180°

Explanation:

Sum of interior angles of a polygon = (n - 2) × 180°

(where n is the number of sides)

A hexagon has 6 sides

⇒ Sum of interior angles of a hexagon = (6 - 2) × 180° = 720°

Let x = smallest unknown angle

Therefore, 3x = largest unknown angle

Sum the angles and solve for x:

⇒ 114° + 130° + 140° + 96° + x + 3x = 720°

⇒ 480° + 4x = 720°

⇒ 4x = 720° - 480°

⇒ 4x = 240°

⇒ x = 60°

Therefore, smallest unknown angle = 60°

and largest unknown angle = 3 × 60° = 180°