Mathematics

In the given figure line AB and CD intersect at O . $\angle BOC = {36^ \circ }$. Find $\angle x$ , $\angle y$ and  $\angle z$

SOLUTION
In first figure,
$\angle AOD=\angle BOC$ ------- Vertically Opposite angles
$\therefore x= 36^\circ$

$\angle AOC+\angle COB=180^\circ$ ------ Angles on straight line
$y+36^\circ=180^\circ$
$y=180^\circ-36^\circ$
$y=144^\circ$
$\angle AOC=\angle BOD$ ------- Vertically Opposite angles
$y=z=144^\circ$

In second figure,
$\angle POR+\angle ROT+\angle QOT=180^\circ$ ------ Angles on straight line
$2x+90^\circ+x=180^\circ$
$3x=90^\circ$
$x=30^\circ$
$\therefore 2x= 60^\circ$

$\angle POR=\angle SOQ$ ------- Vertically Opposite angles
$2x=y=60^\circ$

$\angle POS=\angle ROQ$ ------- Vertically Opposite angles
$z=90^\circ+x$
$z=90^\circ+30^\circ$
$z=120^\circ$

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Subjective Medium Published on 09th 09, 2020
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