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The interior angle of a regular polygon is 19 times the size of the exterior angle. calculate the size of the interior angle and the number of sides the polygon has

Respuesta :

Answer:

interior angle = 171° , number of sides = 40

Step-by-step explanation:

let x be the exterior angle , then interior angle = 19x

• sum of exterior angle and interior angle = 180° , then

x + 19x = 180

20x = 180 ( divide both sides by 20 )

x = 9

The exterior angle = 9°

The interior angle = 19x = 19 × 9 = 171°

• sum of the exterior angles of a polygon = 360°

Since the polygon is regular then the exterior angles are congruent (equal)

number of sides = 360° ÷ 9° = 40

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