Home
Class 9
MATHS
Given /P O R=3x a n d /Q O R=2x+10 , fin...

Given `/_P O R=3x a n d /_Q O R=2x+10 ,` find the value of `x` for which `P O Q` will be a line

Text Solution

Verified by Experts

Since QOR, POP are linear pairs
`/_OOR+/_POR = 180^@`
`2x +10+3x =180^@[: /_ QOR =2x+10, POR = 3x]`
`5x +10 =180 ^@`
` ⇒5x=180^@-10`
`⇒5x=170^@`
`⇒x=34^@`
Promotional Banner

Topper's Solved these Questions

  • LINEAR EQUATIONS IN TWO VARIABLES

    RD SHARMA|Exercise All Questions|104 Videos
  • MEASURES OF CENTRAL TENDENCY

    RD SHARMA|Exercise All Questions|141 Videos

Similar Questions

Explore conceptually related problems

In Fig. 6.43, if P Q_|_P S , P Q|| S R , /_S Q R=28^@ and /_Q R T=65^@ , then find the values of x and y.

In a triangle P Q R , let /_P Q R=30o and the sides P Q and Q R have lengths 10sqrt(3) and 10, respectively. Then, which of the following statement(s) is (are) TRUE? /_Q P R=45o (b) The area of the triangle P Q R is 25sqrt(3) and /_Q R P=120o (c) The radius of the incircle of the triangle P Q R is 10sqrt(3)-15 (d) The area of the circumcircle of the triangle P Q R is 100 pi

Consider two points P and Q with position vectors -> O P=3 -> a-2 -> b and -> O Q= -> a+ -> b Find the position vector of a point R which divides the line joining P and Q in the ratio 2:1, (i) internally, and (ii) externally.

The line x+y=p meets the x- and y-axes at Aa n dB , respectively. A triangle A P Q is inscribed in triangle O A B ,O being the origin, with right angle at QdotP and Q lie, respectively, on O Ba n dA B . If the area of triangle A P Q is 3/8t h of the are of triangle O A B , the (A Q)/(B Q) is equal to (a)2 (b) 2/3 (c) 1/3 (d) 3

If x # y = (x + y)/(xy) , then the value of P # (q # r) for every p, q, in N :

In Figure, P Q R S is a parallelogram, P O\ a n d\ Q O are, respectively, the angle bisectors of /_P\ a n d\ /_Q . Line L O M is drawn parallel to P Q . Prove that: P L=Q M (ii) L O=O M

In Figure, /_Q P R=\ /_P Q R\ a n d\ M\ a n d\ N are respectively on sides Q R\ a n d\ P R of P Q R\ such that Q M=P Ndot Prove that O P=O Q , where O is the point of intersection of P M\ a n d\ Q N

P is a point on positive x-axis, Q is a point on the positive y-axis and ' O ' is the origin. If the line passing through P\ a n d\ Q is tangent to the curve y=3-x^2 then find the minimum area of the triangle O P Q , is 3 (b) 4 (c) 5 (c) 6

L, M, N,O, P, Q, R and S are sitting around a circle facing the centre. N, who is third to the left of P, is not a neighbour of M. S is the neighbour of O and R and is third to the right of M. L is not the neighbour of O, who is second to the left of N. If N and O interchange their positions, then which of the following will be the correct statement? 1) S is on the immediate right of N. 2) R is second to the right of O. 3) O is between L and Q. 4) N is between L and Q. 5) None of these

RD SHARMA-LINES AND ANGLES -All Questions
  1. In Figure, ray O S stand on a line P O Qdot Ray O R and ray O T are an...

    Text Solution

    |

  2. In Figure, A C B is a line such that /D C A=5x\ a n d\ /D C B=4xdot Fi...

    Text Solution

    |

  3. Given /P O R=3x a n d /Q O R=2x+10 , find the value of x for which P O...

    Text Solution

    |

  4. In Figure, a is a greater than b by one third of a right-angle. Find...

    Text Solution

    |

  5. What value of y would make A O B a line in Figure, if /A O C=4y\ a n d...

    Text Solution

    |

  6. If Figure, /A O F\ a n d\ /F O G form a linear pair. /E O B=\ /F O C=9...

    Text Solution

    |

  7. In Figure, O P ,\ O Q ,\ O R\ a n d\ O S are four rays. Prove that /...

    Text Solution

    |

  8. In Figure, ray O S stand on a line P O Qdot Ray O R and ray O T are an...

    Text Solution

    |

  9. Lines P Q and R S intersect each other at point Odot If /P O R:/R O...

    Text Solution

    |

  10. In Figure, P O Q is a line. Ray O R is perpendicular to lien P QdotO...

    Text Solution

    |

  11. In Figure, A B C D is a rectangle. Find the values of xa n dydot

    Text Solution

    |

  12. In Figure, determine the value of ydot

    Text Solution

    |

  13. In Figure, three coplanar lines intersect in a common point, forming...

    Text Solution

    |

  14. In figure, A B\ a n d\ C D are straight lines and O P\ a n d\ O Q are ...

    Text Solution

    |

  15. In Figure, two straight lines P Q\ a n d\ R S intersect each other a...

    Text Solution

    |

  16. In Figure, lines l1a n d\ L2\ i ntersect \ at \ O, forming angles as ...

    Text Solution

    |

  17. In Figure, three coplanar lines intersect at a point O , forming ang...

    Text Solution

    |

  18. In Figure, find the value of x ,\ y\ a n d\ z

    Text Solution

    |

  19. In Figure, find the value of x

    Text Solution

    |

  20. Prove that the bisectors of a pair of vertically opposite angles are i...

    Text Solution

    |