Question

Prove that a regular polygon has five sides, if its exterior angle is two third of its interior angle

Answer 1

Given: 

Exterior ∠= 2/3 of interior∠

Exterior ∠ + interior adjacent  ∠ + 180°

Exterior ∠ = 360°/ n                              ( n= no. of sides)

Each interior ∠ = 180 - exterior ∠

Each interior ∠ = 180 - 360° /n

A.T.Q

Exterior ∠= 2/3 of interior∠

360°/ n  = 2/3 ( 180° - 360° /n)

360°/ n = 2/3 ×180° - 2/3 × 360°/n

360°/ n = 120° - 240° /n

360°/ n  +240°/n = 120°

600 °/n =120°

n= 600°/120°

n= 5
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Hence polygon has 5 sides....

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Hope this will help you.....

Answer 2

Answer:

5 sides

Step-by-step explanation:

A.T.Q ( According To The Question)

Exterior ∠= 2/3 of interior∠

360°/ n  = 2/3 ( 180° - 360° /n)

360°/ n = 2/3 ×180° - 2/3 × 360°/n

360°/ n = 120° - 240° /n

360°/ n  +240°/n = 120°

600 °/n =120°

n= 600°/120°

n= 5