Question

Two complementary angles are such that two times the measure of one is equal to three times the measure of the other. The measure of the smaller angle is
A. 45°
B. 30°
C. 36°
D. None of these

Answer 1

Answer : Option C

Explanation,

Let the measures of two angles be x and y .

according to question :

The sum of angles is 90° as they are complementary angles:

x + y = 90° ( equation 1 )

and,

2x = 3y

or 2x - 3y = 0 ( equation 2 )

Now,

multiplying ( equation 1 ) with 2 and ( equation 2 ) with 1.

Then,

2x + 2y = 180 ( equation 3 )

and,

2x - 3y = 0 ( equation 4 )

Subtracting ( equation 1 ) from ( equation ) 2 we get,

2x - 3y = 0

2x + 2y = 180

- - -

0 - 5y = - 180

or, 5y = 180

or, y = 36 ( equation 5 )

Putting the value of ( equation 5 ) in ( equation 1 ) we get,

x + y = 90

x + 36 = 90

x = 90 - 36

x = 54

Therefore, value of x = 54 and value of y = 36.

Hence the measure of smaller angle is 36.

So, The answer will be Option c.

I hope it helps you !!

Answer 2

Answer:

36 is the correct answer please mark me as Brainliest