Question

the exterior angle of a polygon is x degree and interior angles is 8x degree find number of sides it have

Answer 1

Answer:

Step-by-step explanation:

we all know that ext. angles and int. angles make a sum of 180° degrees.

so we have x° and 8x°

x+8x=180

everytime x means 1

1+8x=9x

9x=180

we divide them

x=180÷9

we divide by 9 so it will be 20.

sum of ext. angles of a regular polygon is always 360°

so we divide 360 by 20

360÷20

= 18

Answer 2

Number of sides of the polygon = 18

Given :

The exterior angle of a polygon is x° and interior angles is 8x°

To find :

Number of sides of the polygon

Solution :

Step 1 of 2 :

Calculate measure of each exterior angle

Here it is given that exterior angle of a polygon is x° and interior angles is 8x°

We know that sum of the exterior and interior angle must equal to 180°

∴ x° + 8x° = 180°

⇒ 9x° = 180°

⇒ 9x = 180

⇒ x = 20

∴ Measure of each exterior angle = x° = 20°

Step 2 of 2 :

Find number of sides of the polygon

Number of sides of the polygon

$\displaystyle \sf = \frac{360 {}^{ \circ} }{Measure \: of \: each \: exterior \: angle}$

$\displaystyle \sf = \frac{360 {}^{ \circ} }{{20}^{ \circ}}$

$= 18$

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