wxyz is a cyclic quadrilateral prove that wzy+wxy =180
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Answer:
Sum of opposite angles of a cyclic quadrilateral being
180
∘
we have for cyclic quadrilateral
W
X
Y
Z
∠
X
W
Z
+
∠
X
Y
Z
=
180
∘
⇒
1
2
∠
X
W
Z
+
1
2
∠
X
Y
Z
=
1
2
×
180
∘
⇒
∠
X
W
A
+
∠
X
Y
B
=
90
∘
[ since WA and YB are bisectors of
∠
X
W
Z
and
∠
X
Y
Z
respectively.]
Bur
∠
X
W
A
=
∠
X
Y
A
, being the angles on same arc
A
X
So We have
∠
X
Y
A
+
∠
X
Y
B
=
90
∘
⇒
∠
A
Y
B
=
90
∘
This means
A
B
must be diameter of the circle
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