Question

the sum of an angle is two third of it's complement find the angle

Answer 1

Solution:-

There is a mistake in this question. It should be like this - The measure of an angle is two third of it's complement.

Let one of the complementary angles be 'x'
Then the other angle will be 2x/3

As we know that the two angles are complementary when they add up to 90 degrees.
So, according to the question.

x + 2x/3 = 90°

Taking L.C.M. and solving it, we get.
(3x + 2x)/3 = 90
5x/3 = 90
5x = 90*3
5x = 270
x = 270/5
x = 54

So. measure of one of the angles is 54° and the other is
90 - 54 = 36°

Answer.

Answer 2

If two angels are complementary then the sum of their measure is always 90°

So assume angle 1 is = a°
Then angle 2 will be = ⅔ X a = 2a/3

angle1 + angle2 = 90°
a° + 2a/3 = 90°
(3a + 2a)/3 = 90°
5a = 90 X 3
5a = 270
a = 270/5
a = 54
So angle1 = a = 54°
and angle2 = ⅔Xa = 36°

angle1 + angle2 = 54+36 = 90
So they are complementary angles.