Question

The measure of one interior angle is 108 deg. Find the
number of sides.

Answer 1

Given

• Measure of one interior angle = 108°

To find

• The number of sides.

Solution

Using formula,

★ Exterior angle + Interior angle = 180°

Substituting the given values,

⟼ Exterior angle + 108° = 180°

⟼ Exterior angle = 180° - 108°

⟼ Exterior angle = 72°

★ Exterior angle of the polygon = 72°

Formula to be used :-

★ Number of sides = 360°/Exterior angle

Substituting the given values,

⟼ Number of sides = 360°/72°

⟼ Number of sides = 5

❖ Number of sides of the polygon = 5 sides.

______________________________

Know More

• Sum of interior angles of a polygon =

 (2n - 4) × 90°

❖ 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.

Answer 2

Measure of each interior angle=$( \frac{360}{n} )$

Since, the measure of each interior angle is=108°

Measure of each interior angle=180°-108°=72°

$\frac{360}{n} = 72$

$n = \frac{360}{72} = 5$

Thus, required sides of a regular polygon=5

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