Home
Class 9
MATHS
In the given figure, if x+y=z+w then pro...

In the given figure, if `x+y=z+w` then prove that AOB is a line.

Text Solution

Verified by Experts

We kanow that the sum of all the angles around a point is `360^(@)`.
`:. x+y+z+w=360^(@)`
`implies (x+y)+(z+w)=360^(@)`
`implies (x+y)+(x+y)=360^(@)" "[ :' z+w=x+y]`
`implies 2(x+y)=360^(@) implies x+y=180^(@)`.
Hence, AOB is a straight line.
Promotional Banner

Topper's Solved these Questions

  • LINES AND ANGLES

    RS AGGARWAL|Exercise Example|13 Videos

  • LINES AND ANGLES

    RS AGGARWAL|Exercise Exercise 7A|12 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 Figure,if x+y=2+z, then prove that AOB is a line.

In Figure,if x+y=w+z, then prove that AOB is a line Fig.

In Fig.6.16, if x+y=w+z, then prove that AOB is a line

In Fig. 6.16, if x+y=w+z , then prove that AOB is a line.

In the given figure, it is given that AOB is a straight line and 4x = 5y. What is the value of x?

In the given figure, find angle AOB .

In the given figure, what value of x will make AOB a straight line?

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.

In the given figure, AOB is a straight line. The value of x is

In the given figure, AOB is a straight line. If angleAOC=4x^(@) and angleBOC=5x^(@) then angleAOC=?

RS AGGARWAL-LINES AND ANGLES-Multiple Choice Questions (Mcq)
  1. In the given figure, if x+y=z+w then prove that AOB is a line.

    Text Solution

    |

  2. If one angle of a triangle is equal to the sum of the other two angles...

    Text Solution

    |

  3. An exterior angle of a triangle is 110^(@) and its two interior opposi...

    Text Solution

    |

  4. The angles of a triangle are in the ratio 3 : 5 : 7. The triangle is

    Text Solution

    |

  5. If one of the angles of a triangle is 130^(@) then the angle between t...

    Text Solution

    |

  6. In the given figure, AOB is a straight line. The value of x is

    Text Solution

    |

  7. The angles of a triangle are in the ratio 2 : 3 : 4. The largest angle...

    Text Solution

    |

  8. In the given figure, angleOAB=110^@ and angleBCD=130^(@) then angleABC...

    Text Solution

    |

  9. If two angles are complementary to each other, then each angle is :

    Text Solution

    |

  10. An angle which measures more than 180^(@) but less than 360^(@), is ca...

    Text Solution

    |

  11. The measure of an angle which is five times its complement. The angle ...

    Text Solution

    |

  12. Two complementary angles are such that twice the measure of the one is...

    Text Solution

    |

  13. In the given figure, AOB is a straight line. If angleAOC=4x^(@) and an...

    Text Solution

    |

  14. In the given figure, AOB is a straight line. If angleAOC=(3x+10)^(@) a...

    Text Solution

    |

  15. In the given figure, AOB is a straight line. If angleAOC=(3x-10)^(@), ...

    Text Solution

    |

  16. Which of the following statements is false ?

    Text Solution

    |

  17. An angle is one fifth of its supplement. The measure of the angle is

    Text Solution

    |

  18. In the adjoining figure, AOB is a straight line. If x:y:z=4 : 5 : 6, t...

    Text Solution

    |

  19. In the given figure, straight lines AB and CD intersect at O. If angle...

    Text Solution

    |

  20. straight lines AB and CD intersect at O. If angleAOC+angleBOD=130^(@) ...

    Text Solution

    |

  21. In the given figure, AB is a mirror, PQ is the incident ray and QR is ...

    Text Solution

    |