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In Figure, /P Q R=\ /P R Q , then prove ...

In Figure, `/_P Q R=\ /_P R Q ,` then prove that `/_P Q S=\ /_P R Tdot`

Text Solution

Verified by Experts

`anglePQS+anglePQR=180^o`-(1)
`anglePRQ+anglePRT=180^o`-(2)
`anglePQR=anglePRQ`(given)
`anglePQR+anglePRT=180^o`
`anglePQR=180^o-anglePRT`
putting this value in equation (1)
`anglePQS+180^o -anglePRT=180^o`
`anglePQS=anglePRT`
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RD SHARMA-LINES AND ANGLES -All Questions
  1. In Fig. 6.13, lines AB and CD intersect at O. If /A O C\ +/B O E=70^@...

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  2. In Figure, lines X Y\ a n d\ M N intersect at O. If /P O Y=90^0a n d\ ...

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  3. In Figure, /P Q R=\ /P R Q , then prove that /P Q S=\ /P R Tdot

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  4. If ray O C stands on line A B such that /A O C=/C O B , then show that...

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

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  6. It is given that ∠XYZ = 64° and XY is produced to point P. Draw a figu...

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  7. Prove that ,The bisectors of base angles of a triangle cannot enclos...

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  8. Name the pairs of adjacent angles in the figures given below :

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  9. In figure, DeltaO D C DeltaO B A ,/B O C=125^oand /C D O=70^o. Find...

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  10. O A\ =\ O Ba n d\ O D\ =\ O C. Show that (i) DeltaA O D~=DeltaB O C a...

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  11. A B C D is a cyclic quadrilateral in which: B C A D ,\ /A D C=110^0...

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  12. How many pairs of adjacent angles are formed when two lines intersec...

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  13. How many pairs of adjacent angles, in all, can you name in Figure.

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  14. In the figure ,find the value of x.

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  15. In figure, O is the centre of the circle angleBCO=30^(@) . Find X an...

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

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

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

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

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

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