Question

If the measure of an angle is 78 less than the measure of its compliment, what is the measure of the angle?

Answer 1

Complementary angles add up to 90'
So let X= angle 1
Y=angle 2
So x+y=90
let x=y-78
so(y-78)+y=90
y-78+y=90
2y-78=90
2y=90+78
2y=168
y=168/2
y=84
x=y-78
so x=84-78
x=6
And 6+84=90
So the measure of the angle is 6 degrees.
Hope i helped!

Answer 2

Measure of the angle is 6°

Explanation:

let x be the measure of compliment.

The angle = 90 - x

We know that sum of an angle and its compliment is equal to 90°.

So, According to the Question

90 - x = x - 78

90 + 78 = x + x (transpose 78 to LHS and x to RHS )

x + x = 90 + 78

2x = 168

x = 84

So, Angle = 90 - x = 90- 84 = 6

Therefore, Measure of the angle is 6°