Question

For the given figure, find the angle ∠ZVY.

degrees.

Answer 1

The figure consists of 3 circles: large, medium and small.

XYVW is a cyclic quadrilateral to the large circle.
As opposite angles of a cyclic quadrilateral have a sum of ${180}^o,$
$\angle YVW={180}^o-\angle X$
$\Rightarrow \angle YVW={180}^o-{95}^o={85}^o$

Connect the intersection points of the medium and small circle.

XABW is a cyclic quadrilateral to the small circle.
$\therefore \angle XAB={180}^o-\angle W$
$\Rightarrow \angle XAB={180}^o-{84}^o={96}^o$

XAZ is a straight line.
$\therefore \angle ZAB={180}^o-\angle XAB={84}^o$

AZVB is a cyclic quadrilateral to the medium circle.
$\therefore \angle ZVB={180}^O-\angle ZAB={96}^o$

$\angle ZVY=\angle ZVB-\angle YVB$
$\Rightarrow \angle ZVY={96}^o-{85}^o={11}^o$