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White raven [17]
3 years ago
5

The angles of a pentagon are x, x − 5 0 , x + 100 , 2x + 150and 2x + 300 . Find all the angles.

Mathematics
1 answer:
miv72 [106K]3 years ago
8 0

Answer:

The interior angles are 70°,65°,80°,155° and 170°

Step-by-step explanation:

step 1

Find the sum of the interior angles of the pentagon

The sum is equal to

S=(n-2)*180°

where

n is the number of sides of polygon

n=5 (pentagon)

substitute

S=(5-2)*180°=540°

step 2

Find the value of x

Sum the given angles and equate to 540

x+(x-5)+(x+10)+(2x+15)+(2x+30)=540°

7x+50=540°

7x=490°

x=70°

step 3

Find all the angles

x=70°

(x-5)=(70-5)=65°

(x+10)=(70+10)=80°

(2x+15)=(2*70+15)=155°

(2x+30)=(2*70+30)=170°

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