Home
Class 9
MATHS
In the given figure, lines XY and LM int...

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.

A

`144^(@)`

B

`126^(@)`

C

`90^(@)`

D

`54^(@)`

Text Solution

Verified by Experts

The correct Answer is:
A
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^(@)`.
Doubtnut Promotions Banner Mobile Dark
|

Topper's Solved these Questions

  • LINES AND ANGLES

    RS AGGARWAL|Exercise Exercise 7A|12 Videos

  • LINES AND ANGLES

    RS AGGARWAL|Exercise Exercise 7B|16 Videos

  • LINES AND ANGLES

    RS AGGARWAL|Exercise Multiple Choice Questions (Mcq)|28 Videos

  • LINEAR EQUATIONS IN TWO VARIABLES

    RS AGGARWAL|Exercise Multiple Choice Questions (Mcq)|24 Videos

  • MEAN , MEDIAN AND MODE OF UNGROUPED DATA

    RS AGGARWAL|Exercise Multiple Choice Questions (Mcq)|18 Videos

Similar Questions

Explore conceptually related problems

In the given figure, lines XY and MN intersect at O. If anglePOY=90^(@) and a:b=2:3 ,then find c.

In Figure,lines XY and MN intersect at O. If /_POY=90^(@) and A:B=2:3, find c

In the given figure, name: lines whose point of intersection is C

In the figure given below, lines XY and MN intersect at O If anglePOY=90^(@) and a:b =2:3, then find the measure of c.

In the given figure if c=3b and a=5b find the value of a and b

In the given figure, find the value of x in terms of a, b and c.

In fig: 6.14, lines XY and MN intersect at O. If /_P O Y=90^@ and a : b=2:3 , find c.

In the given figure , PQ and RS intersect each other at O . If angleSOT=75^(@) , find the values of a , b and c .

In the given figure, the two lines AB and CD intersect at a point O such that angleBOC=125^(@) . Find the values of x, y, and z.

From the given figure,find the values of a,b, c,and d.

Home
Profile