Math, asked by gabrielleberry100, 3 months ago

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

Answers

Answered by AestheticSoul
5

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.

Answered by Anonymous
34

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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