Question

The exterior angle of a regular polygon is 90° less than the interior angle.Find the size of each exterior angle?

Answer 1

Given :-

The exterior angle of a regular polygon is 90° less than the interior angle.

To Find :-

Exterior angle of a polygon.

Solution :-

Given that,

The exterior angle of a regular polygon is 90° less than the interior angle.

Let

• Interior angle of regular polygon be 'x'.

So,

• Exterior angle of regular polygon be 'x - 90°'

We know that,

★ In regular polygon,

★ Interior angle + Exterior angle = 180°.

x + x - 90° = 180°

2x = 180° + 90°

2x = 270°

x = 135°.

Hence,

• Exterior angle = x - 90° = 135° - 90° = 45°.

Additional Information :-

$\boxed{ \sf{ \: Exterior \: angle = \dfrac{360}{number \: of \: sides} }}$

$\boxed{ \sf{ number \: of \: sides = \dfrac{360}{Exterior \: angle} }}$

$\boxed{ \sf{ \:Sum \: of \: Exterior \: angles = 360 \degree }}$

$\boxed{ \sf{ \:Sum \: of \: interior \: angles = (2n - 4) \times 90 \degree }}$