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

75^{o}

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100^{o}

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120^{o}

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105^{o}

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Solution

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

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

The correct option is D 105oLet X and Y be two supplementary angles. We know X+Y=180∘ ............(1)Let Y be greater angle. Y=2X−45∘ as per the question ...........(2)From (1) and (2), we haveX+2X−45=180⇒3X=225∘⇒X=75∘Thus Y=180−75=105∘ ....It is the largest angle.

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