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Byju's Answer
Standard IX
Mathematics
Opposite Sides of a Parallelogram Are Equal
The average o...
Question
The average of
3
angles of a quadrilateral which are in the ratio of
2
:
4
:
5
is
77
o
. Find all the angles of the quadrilateral.
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Solution
Let
2
x
,
4
x
and
5
x
be the
3
angles of given quadrilateral and
m
be the fourth angle of the same quadrilateral.
Therefore,
2
x
+
4
x
+
5
x
3
=
77
⇒
11
x
=
231
⇒
x
=
231
11
=
21
Therefore,
2
x
=
2
×
21
=
42
4
x
=
4
×
21
=
84
5
x
=
5
×
21
=
105
The three angles of the quadrilateral are
42
o
,
84
o
and
105
o
.
Therefore,
As we know that sum of internal angles of a quadrilateral is
360
o
.
∴
42
+
84
+
105
+
m
=
360
⇒
m
=
360
−
231
=
129
o
Hence the angles of the given quadrilateral are
42
o
,
84
o
,
105
o
and
129
o
.
'
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