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In a cyclic quadrilateral
MATHEMATICS · Multi-part · CBSE · Mathematics · Circles · Circles
Problem
In a cyclic quadrilateral
W
X
Y
Z
WXYZ
W
X
Y
Z
, the angles are given by
∠
W
=
(
2
x
+
15
)
∘
\angle W = (2x + 15)^{\circ}
∠
W
=
(
2
x
+
15
)
∘
,
∠
Y
=
(
3
x
−
5
)
∘
\angle Y = (3x - 5)^{\circ}
∠
Y
=
(
3
x
−
5
)
∘
,
∠
X
=
(
2
y
−
10
)
∘
\angle X = (2y - 10)^{\circ}
∠
X
=
(
2
y
−
10
)
∘
, and
∠
Z
=
(
y
+
25
)
∘
\angle Z = (y + 25)^{\circ}
∠
Z
=
(
y
+
25
)
∘
. (a) Find the value of
x
x
x
. (b) Find the value of
y
y
y
. (c) Hence determine the measure of
∠
Z
\angle Z
∠
Z
.
Related theory
Cyclic Quadrilaterals
Circles
Cyclic quadrilateral properties
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