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Question
Two angles are making a linear pair. If one of them is one-third of the other, find the angles.
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Solution
Let one angle be x.
It is given that other angle is one-third of first.
So, other angle will be `1/3 x`.
Again, given that both the angles are making a linear pair.
So, their sum will be 180°.
∴ `x + 1/3 x = 180^circ`
⇒ `(3x + x)/3 = 180^circ` ...[Taking LCM of 1 and 3 on LHS]
⇒ `(4x)/3 = 180^circ`
⇒ `x = (180^circ xx 3)/4`
⇒ x = 135°
Hence, the angles are 135° and `1/3 xx 135^circ`, i.e. 135° and 45°.
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