Question

For the given figure, find the angle $\angle XWU.$

• A. ${89}^o$
• B. ${90}^o$
• C. ${91}^o$

Answer 1

The correct option is C ${91}^o$

For the triangle $△UYZ,$
$\angle Y+\angle Z+\angle U={180}^o$
$\Rightarrow \angle Y+{59}^o+{30}^o={180}^o$
$\Rightarrow \angle Y={180}^o-{59}^o-{30}^o={91}^o$

We know that opposite angles of a cyclic quadrilateral have a sum of ${180}^o.$

For cyclic quadrilateral $ZWXY,$
$\angle Y+\angle XWZ={180}^o$
$\Rightarrow \angle XWZ={180}^o-\angle Y={180}^o-{91}^o$
$\Rightarrow \angle XWZ={89}^o$

$\angle UWZ$ is a straight angle.
$\therefore \angle UWX+\angle XWZ={180}^o$
$\Rightarrow \angle UWX={180}^o-\angle XWZ$
$\Rightarrow \angle UWX={180}^o-{89}^o={91}^o$