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Standard VIII
Mathematics
Angle Sum Property of a Polygon
Question
Find the unknown angle
x
in the above figure.
60
0
120
0
108
0
90
0
A
60
0
B
120
0
C
90
0
D
108
0
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Solution
Verified by Toppr
The given figure is a regular pentagon since it has
5
sides and all are equal
We know that the sum of the internal angles
S
n
of an
n
sided convex polygon is
(
n
−
2
)
×
180
o
Here
n
=
5
,
i.e
S
n
=
(
5
−
2
)
×
180
o
=
540
o
.
.
.
.
.
.
.
(
i
)
In a regular polygon, all the sides are equal and all the angles are equal to each other
∴
5
x
=
540
o
⇒
x
=
108
o
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