Question

Question 2
In the given figure, lines XY and MN intersect at O. If $\angle POY={90}^{\circ }$ and a:b = 2:3, find c.

Answer 1

Let the common ratio between a and b be x.
a = 2x and b = 3x
XY is a straight line, rays OM and OP stand on it.
$\therefore \angle XOM+\angle MOP+\angle POY={180}^{\circ }$
$b+a+\angle POY={180}^{\circ }$
$3x+2x+{90}^{\circ }={180}^{\circ }$
$5x={90}^{\circ }$
$x={18}^{\circ }$
$a=2x=2\times 18={36}^{\circ }$
$b=3x=3\times 18={54}^{\circ }$
MN is a straight line. Ray OX stands on it.
$\therefore b+c={180}^{\circ }$ ( Linear pair)
${54}^{\circ }+c={180}^{\circ }$
$c={180}^{\circ }–{54}^{\circ }={126}^{\circ }$
$\therefore c={126}^{\circ }$