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The supplement of an angle is one-third ...

The supplement of an angle is one-third of itself. Determine the angle and its supplement.

A

`110^@` , `30^@.`

B

`135^@` , `45^@.`

C

`125^@` , `35^@.`

D

`140^@` , `40^@.`

Text Solution

Verified by Experts

The correct Answer is:
B
Let the qangle is `theta`. Then, its supplement will be `180-theta`.
It is given that,
`180-theta = 1/3 theta`
`=>540-3theta = theta`
`=>4theta = 540`
`=>theta = 135`
So, angle is `135^@` and its supplement is `45^@.`
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RD SHARMA-LINES AND ANGLES -All Questions
  1. Two supplementary angles are in the ratio 4:5 . Find the angles.

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  2. If an angle is 28^@ less than its complement, find its measure.

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  3. The supplement of an angle is one-third of itself. Determine the an...

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

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  5. An angle is 14^@ more than its complementary angle. What is its measur...

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  6. If an angle differs from its supplement by 10^@ , find the angle.

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  7. In Fig. 6.17, POQ is a line. Ray OR is perpendicular to line PQ. OS ...

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  8. Find the angle which is equal to its complement

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  9. Find the measure of an angle which forms a pair of supplementary ang...

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  10. Two supplementary angles differ by 34^0 . Find the angles.

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  11. An angle is equal to five times its complement. Determine its measu...

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  12. An angle is equal to one-third of its supplement. Find its measure.

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  13. Two supplementary angles are in the ratio 2:3. Find the angles.

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  14. The supplement of an angle is one-third of itself. Determine the an...

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  15. Write the complement of each of the following angles: (i) 20^0 (ii) ...

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  16. Write the supplement of each of the following angles: (i) 54^0 (ii) ...

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  17. If an angle is 28^0 less than its complement, find its measure.

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  18. If an angle is 30^0 more than one half of its complement, find the ...

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  19. Two supplementary angles are in the ratio 4:5 . Find the angles.

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  20. Two supplementary angles differ by 48^0 . Find the angles.

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