Mathematics

An angle is $$45^o$$ less than two times of its supplement, then the greater angle is ___________.


ANSWER

$$105^o$$


SOLUTION
Let $$X$$ and $$Y$$ be two supplementary angles. 
 We know $$X+Y= 180^{\circ}$$     ............(1)
Let $$Y$$ be greater angle. 
$$Y= 2X-45^{\circ}$$  as per the question      ...........(2)
From (1) and (2), we have
$$X+2X-45=180$$
$$\Rightarrow 3X= 225^{\circ}$$
$$\Rightarrow X= 75^{\circ}$$
Thus $$ Y=180-75= 105^{\circ}$$ ....It is the largest angle.
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