Question

The angles of a polygon are x ◦, (x − 10) ◦, (x + 20) ◦, (2x − 44) ◦, (2x − 70) ◦respectively. Find its interior angles.

Answer 1

Answer:

From the question it is given that, angles of a pentagon are

x

0

,(x−10)

∘

,(x+20)

∘

,(2x−44)

∘

and (2x−70)

∘

We know that, Sum of measures of all interior angles of polygons =(2n−4)×90

∘

Where, n=5

=((2×5)−4)×90

∘

=(10−4)×90

∘

=6×90

∘

=540

∘

Then, x

0

+(x−10)

0

+(x+20)

0

+(2x−44)

0

+(2x−70)

0

=540

x+x−10

0

+x+20

0

+2x−44

0

+2x−70

0

=540

∘

7x+20

∘

−124

∘

=540

∘

7x−104

∘

=540

∘

By transposing we get,

7x=540

∘

+104

∘

7x=644

∘

x=644

∘

/7

x=92

∘

Therefore, the value of x is 92

∘

.