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Standard IX
Mathematics
Question
If
P
Q
⊥
P
S
,
P
Q
∥
S
R
,
∠
S
O
R
=
28
o
and
∠
Q
R
T
=
65
o
, then find
x
&
y
.
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Solution
Verified by Toppr
∵
P
Q
∥
S
R
∠
P
Q
R
=
∠
Q
R
T
(Alternate interior angle)
⇒
x
+
28
∘
=
65
∘
⇒
x
=
65
∘
−
28
∘
⇒
x
=
37
∘
I
n
Δ
P
Q
S
∠
P
+
∠
Q
+
∠
S
=
108
∘
(By angle sum property)
⇒
90
∘
+
x
+
y
=
180
∘
⇒
90
∘
+
37
∘
+
y
=
180
∘
⇒
y
=
108
∘
−
127
⇒
y
=
53
∘
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If
P
Q
⊥
P
S
,
P
Q
∥
S
R
,
∠
S
O
R
=
28
o
and
∠
Q
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T
=
65
o
, then find
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.
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o
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