Question

In given figure, lines XY and MN intersect at O. If ∠POY = 90° and a : b = 2 : 3, find c.​

Answer 1

Since XY is a straight line,
$\angle POY+a+b={180}^{\circ }$
Putting the value of $\angle POY={90}^{\circ }$ (Given)
Hence, we get,
$a+b={90}^{\circ }$
Now, a : b = 2 : 3 (Given)
Let a be ${}^{\prime }2x^{\prime }$ and b be ${}^{\prime }3x^{\prime }$
$\therefore 2x+3x={90}^{\circ }$
$\Rightarrow 5x={90}^{\circ }\Rightarrow x={18}^{\circ }$
$\therefore a=2\times {18}^{\circ }={36}^{\circ }$
Similarly,
$b=3\times {18}^{\circ }={54}^{\circ }$
From the diagram, $b$ and $c$ form a linear pair,
$\therefore b+c={180}^{\circ }$
${54}^{\circ }+c={180}^{\circ }$
$\therefore c={126}^{\circ }$