Question

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Answer 1

Answer:

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Answer 2

Given :

• A polygon with two exterior angle of 70° and 60° and interior angle 2x , 2x and 30°.

To Find :

• Value of x.

Solution :

$\longmapsto\tt{y+70=180\degree\:(Linear\:Pair)}$

$\longmapsto\tt{y=180\degree-70\degree}$

$\longmapsto\tt\bold{y=110\degree}$

Similarly ,

$\longmapsto\tt{z+60\degree=180\degree\:(Linear\:Pair)}$

$\longmapsto\tt{z=180\degree-60\degree}$

$\longmapsto\tt\bold{z=120\degree}$

Now ,

As we know that sum of all angles of a polygon is 540°.So ,

$\longmapsto\tt{30\degree+2x+2x+y+z=540\degree}$

$\longmapsto\tt{30\degree+4x+110\degree+120\degree=540\degree}$

$\longmapsto\tt{260\degree+4x=540\degree}$

$\longmapsto\tt{4x=540\degree-260\degree}$

$\longmapsto\tt{4x=280\degree}$

$\longmapsto\tt{x=\cancel\dfrac{280}{4}}$

$\longmapsto\tt\bold{x=70\degree}$

So , The value of x is 70°

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VERIFICATION :

$\longmapsto\tt{30\degree+2(70)+2(70)+110\degree+120\degree=540\degree}$

$\longmapsto\tt{30\degree+140\degree+140\degree+110\degree+120\degree=540\degree}$

$\longmapsto\tt\bold{540\degree=540\degree}$

HENCE VEDIFIED