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Byju's Answer
Standard VIII
Mathematics
Classification of Polygons on the Basis of Number of Sides / Vertices
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Question
Find the number of sides in a regular polygon if each interior angle is four times the adjacent exterior angle
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Solution
The sum of exterior angle and its adjacent interior is
180
0
, that is,
e
+
i
=
180
0
Since each interior angle is four times the adjacent exterior angle, therefore, substitute
i
=
4
e
.
e
+
4
e
=
180
0
⇒
5
e
=
180
0
⇒
e
=
180
0
5
=
36
0
We know that the measure of exterior angle is
e
=
(
360
n
)
0
where
n
is the number of sides.
Here, it is given that the exterior angle is
e
=
36
0
, therefore,
n
=
360
e
=
360
36
=
10
Hence, the number of sides is
10
.
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Classification of Polygons on the Basis of Number of Sides / Vertices
Standard VIII Mathematics
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