Four times the complement increased by forty-six is the same as twice the supplement. Find the measures of the angle, the complement, and the supplement. ?

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Answer 1 · 2018-01-22T11:07:18

Let the angle be $x^{\circ}$ $x^@$

So its complement is $(90 - x)$ $(90-x)$ and supplement is $180 - x$ $180-x$

By the problem

$(90 - x) 4 + 46 = 2 (180 - x)$ $(90-x)4+46=2(180-x)$

$\Rightarrow 360 - 4 x + 46 = 360^{- 2} x$ $=>360-4x+46=360^-2x$

$\Rightarrow 4 x - 2 x = 46$ $=>4x-2x=46$

$\Rightarrow 2 x = 46$ $=>2x=46$

$\Rightarrow x = \frac{46}{3} = 23$ $=>x=46/3=23$

So complement $(90 - x) = 90 - 23 = 67$ $(90-x)=90-23=67$

And supplement $180 - x = 180 - 23 = 157$ $180-x=180-23=157$