Question

If all the angles of a hexagon are equal find the measure of each angle
$5 \times 0$
​

Answer 1

Given

• All the angles of hexagon are equal.

To find

• Measure of each angle

Solution

We are given in the question, that the hexagon's all angles are equal. So, it is a regular hexagon.

Regular hexagon ⟶ All angles, all sides are equal.

❖ Formula to be used :-

• Each angle of the hexagon = $\sf\cfrac{(2n - 4) \times 90^{\circ}}{n}$

Where,

• n = number of sides.

Substituting the given values,

$: \implies\sf \cfrac{(2n - 4) \times 90^{ \circ}}{n}$

$: \implies\sf \cfrac{(2 \times 6 - 4) \times 90^{ \circ}}{6}$

$: \implies\sf \cfrac{(12 - 4) \times 90^{ \circ}}{6}$

$: \implies\sf \cfrac{8 \times 90^{ \circ}}{6}$

$: \implies\sf \cfrac{720^{ \circ}}{6}$

$: \implies\sf \cfrac{ \cancel{720^{ \circ}}}{ \not6}$

$: \implies\bf 120^{ \circ}$

$\diamond\boxed {\bf \red{each \: angle \: of \: hexagon = 120^ \circ}}$

___________________________________________

Know More :-

• A regular polygon has :-

1. All its sides equal to each other.
2. All its interior angles equal to each other.
3. All its exterior angles equal to each other.

Some related formulae :-

• Each exterior angle of a regular polygon = $\sf\cfrac{360^{ \circ}}{n}$

• Sum of interior angles of a polygon =

(2n - 4) × 90°

• Exterior angle + Interior angle = 180°