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Byju's Answer
Standard VIII
Mathematics
Kite
In an isoscel...
Question
In an isosceles trapezium
P
Q
R
S
,
∠
P
and
∠
S
are in the ratio
1
:
2
. Find the measure of all the angles.
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Solution
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In an isosceles trapezium base angles are equal;
∠
P
=
∠
Q
.
Let
∠
P
=
x
∘
and
∠
S
=
2
x
∘
.
Since
∠
P
+
∠
S
=
180
∘
(one pair of adjacent angles of a trapezium is supplementary), we get
x
∘
+
2
x
∘
=
180
∘
.
Thus,
3
x
∘
=
180
∘
or
x
∘
=
180
∘
/
3
=
60
∘
.
Hence
∠
P
=
60
∘
and
∠
S
=
2
×
60
∘
=
120
∘
. Since
∠
P
=
∠
Q
, we get
∠
Q
=
60
∘
. But,
∠
Q
+
∠
R
=
180
∘
(one pair of adjacent angles are supplementary).
Hence we also get
∠
R
=
180
∘
−
60
∘
=
120
∘
.
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Q.
In given figure 5.3
□
PQRS is an Isosceles trapezium. Side PQ || side SR and
∆
RQE is an equilateral triangle; find the measures of all the angles of the trapezium.