Question

If an angle is 50° less than one third of its supplement, find the measure of the angle?

Answer 1

GIVEN:-

• An angle is 50° less than one third of its supplement,

TO FIND:-

• The measures of the angles.

Now,

$\rm{Let\:the\:angle\:be\:x}$

then,

$\rm{Supplement\: angle = (180-x)}$

Atq,

$\implies\rm{ \dfrac{1}{3}(180-x) - 50 = x}$

$\implies\rm{\dfrac{1}{\cancel{3}}\times({\cancel{180} - x})- 50 = x}$

$\implies\rm{60 - \dfrac{x}{3} - 50 = x}$

$\implies\rm{ -\dfrac{x}{3} = x +50 - 60}$

$\implies\rm{ -\dfrac{x}{3} = x - 10}$

$\implies\rm{ -\dfrac{x}{3} - x = -10}$

$\implies\rm{ \dfrac{-4x}{3} = -10}$

$\implies\rm{ -4x = -30}$

$\implies\rm{ x = 7.5}$.

Hence , The angle is 7.5°

and Supplement angle = (180-7.5) = 172.5°

Answer 2

Given

1 . An angle is 50° less than one third of its supplement

Answer

Let angle be " x "

So , Supplement angle be " 180 - x "

According to condition ,

$:\to \rm x=\dfrac{1}{3}(180-x)-50\ \; \orange{\bigstar} \\\\:\to \rm x=60-\dfrac{x}{3}-50\\\\:\to \rm x+\dfrac{x}{3}=10\\\\:\to \rm \dfrac{4x}{3}=10\\\\:\to \rm x=\dfrac{30}{4}\\\\:\to \rm x=7.5^{^o}$

So , Measure of the angle = 7.5°