Question

Five angles of a hexagon measure 116°each .What is the measure of the remaining angle

Answer 1

Answer :

Given,

A hexagon ( Note : It's not regular as it is not mentioned in the question )

Five angles of this hexagon are 116° each.

To find,

The sixth angle of this hexagon.

Solution :

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

Sum.of interior angles of hexagon = ( 6 - 2 ) × 180° = 4 × 180° = 720°

Sum of other five angles = 116 × 5 = 580°

Measure of the sixth angle of this hexagon = 720° - 580° = 140°

Answer 2

We  know  that,

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

Where n is  number  is  sides.

Hexagon has  6  sides and  6 interior angle as shown in figure,

Now,

Sum if  its  all 6 angles = (6-2)×180 = 720°

Sum of  Five angles = 116°×5 = 580°

Hence,

6th angle  = 720° - 580° = 140°