Question

The chords XY and YZ are of equal length. These chords are sides of the cyclic quadrilateral WXYZ.The angle ∠YZX is degrees

Answer 1

WXYZ is a cyclic quadrilateral.
$\therefore \angle Y={180}^o-\angle W$
(as opposite angles of cyclic quadrilateral are supplementary angles)
$\angle Y={180}^o-{65}^o={115}^o$

The chords XY and YZ are of equal length.
$\therefore$ For $△XYZ,$
$\angle YXZ=\angle YZX$
(as opposite angles of equal sides have same measure)

From property of sum of interior angles,
$\angle Y+\angle YXZ+\angle YZX={180}^o$
$\Rightarrow 2\angle YXZ={180}^o-\angle Y={180}^o-{115}^o={65}^o$
$\Rightarrow \angle YXZ=\frac{{65}^o}{2}={32.5}^o$