Question

if the complement of an angle is one third of its supplement find the angle

Answer 1

the complement of angle. = ( 90 - x )...... and 1/3 of supplement means. 1/3 ( 180 - x). so. ( 90 - x ). = 1/3 ( 180 - x ). solve it. and the answer will be 45

Answer 2

$\huge{\underline{\underline{\huge{\bold{AnsweR \: :-}}}}}$

Consider the required angle as ${x}^{o}$

We know that the complement can be written as ${90}^{o} - {x}^{o}$and the supplement can be written as ${180}^{o} - {x}^{o}$

To find the measure of an angle is equal to its complement

We get

$[ {90}^{o} - {x}^{o} ]= \frac{1}{3} [ {180}^{o}- {x}^{o} ]$

We can also write it as

$[ {90}^{o} - {x}^{o}]=60- \frac{1}{3} {x}^{o}$

So, we get

${x}^{o} - \frac{1}{3} {x}^{o} ={90}^{o} - {60}^{o}$

$\frac{2}{3} {x}^{o} = {30}^{o}$

By division we get

$x = \frac{(30 \times 3)}{2}$

$x = {45}^{o}$

Therefore the measure of an angle which is one third of its supplement is 45°