In the given figure, lines XY and LM intersect at O. If `angleXOL=a, angleLOP=b, anglePOY=90^(@), angleXOM=c` and `a : b=2 : 3`, find the value of c.

Options

A. `144^(@)`
B. `126^(@)`
C. `90^(@)`
D. `54^(@)`

Answer

A

Explanation

It is given that `a : b= 2: 3`
So, let `a=(2x)^(@) and b=(3x)^(@)`.
In the given figure, ray OP stands on line XY.
`:. angleXOP+anglePOY=180^(@)`
`implies angleXOL+angleLOP+90^(@)=180^(@)" "[ :' anglePOY=90^(@)]`
`implies a+b+90=180`
`implies a+b=90`
`implies 2x+3x=90 implies 5x=90 implies x=18`.
`:. a=(2x)^(@)=(2xx18)^(@)=36^(@) and b=(3x)^(@)=(3xx18)^(@)=54^(@)`.
Again, ray OX stands on line LM.
`:. amgleLOX+angleXOM=180^(@)`
`implies a+c=180^(@)`
`implies 36^(@)+c=180^(@) implies c=(180^(@)-36^(@))=144^(@)`.
Hence, `c=144^(@)`.