Question

find the measure of an angle.1.equal to its complement.2.equal to its supplement,with solution

Answer 1

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Let the angle be x

(1) Complement of x = x

✒ 90-x = x

✒ 90 = x+x

✒ 90 = 2x

✒ 90/2 = x

✒ 45° = x


(2) Supplement of x = x

✒ 180-x = x

✒ 180 = x+x

✒ 180 = 2x

✒ 180/2 = x

✒ 90° = x

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Answer 2

1) Let the angle be x. 
The complement of angle x is (90-x). 
Now, we have to find such an angle x which is equal to its complement. 
$x = (90-x)[tex] [tex]x=90-x$
$x+x = 90-x+x$
$2x = 90$
$\frac{2x}{2} = \frac{90}{2}$
$x = 45$
∴ Angle 45° is equal to its complement. 

2) Let the angle be y. 
Supplement of y = (180-y)
Now, we have to find such an angle y which is equal to its supplement. 
$y = (180-y)$
$y=180-y$
$y+y=180-y+y$
$2y=180$
$\frac{2y}{2} = \frac{180}{2}$
$y=90$
∴ Angle 90° is equal to its supplement. 

Hope this may help you.