In the given figure line AB and CD intersect at O. angle BOC = 36. Find angle x angle y angle z
Fig. Q.10
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Answer:
In first figure,
∠
A
O
D
=
∠
B
O
C
------- Vertically Opposite angles
∴
x
=
36
∘
∠
A
O
C
+
∠
C
O
B
=
180
∘
------ Angles on straight line
y
+
36
∘
=
180
∘
y
=
180
∘
−
36
∘
y
=
144
∘
∠
A
O
C
=
∠
B
O
D
------- Vertically Opposite angles
y
=
z
=
144
∘
In second figure,
∠
P
O
R
+
∠
R
O
T
+
∠
Q
O
T
=
180
∘
------ Angles on straight line
2
x
+
90
∘
+
x
=
180
∘
3
x
=
90
∘
x
=
30
∘
∴
2
x
=
60
∘
∠
P
O
R
=
∠
S
O
Q
------- Vertically Opposite angles
2
x
=
y
=
60
∘
∠
P
O
S
=
∠
R
O
Q
------- Vertically Opposite angles
z
=
90
∘
+
x
z
=
90
∘
+
30
∘
z
=
120
∘
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