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In the given figure , if anglePQR=angleP...

In the given figure , if `anglePQR=anglePRQ` then prove that `anglePQS=anglePRT`.

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Since ray QP stands on line ST, we have
`anglePQR+anglePQS=180^(@)`. ...(i)
Again, ray RP stands on line ST.
`:. anglePRQ+anglePRT=180^(@)`. ...(ii)
From (i) and (ii), we get
`anglePQR+anglePQS=anglePRQ+anglePRT`
`implies anglePRQ+anglePQS=anglePRQ+anglePRT" "[ :' anglePQR=anglePRQ]`
`implies anglePQS=anglePRT`.
Hence, `anglePQS=anglePRT`.
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RS AGGARWAL-LINES AND ANGLES-Multiple Choice Questions (Mcq)
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  2. If one angle of a triangle is equal to the sum of the other two angles...

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

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

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

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

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

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

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

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

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

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

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

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

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

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  16. Which of the following statements is false ?

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

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

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

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

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

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