Question

The sum of complementary angle and the supplementary angle of a given anglebis two times the difference between the supplementary angle and complementary angle what is the measure of that angle

Answer 1

Angle one = x

Other angle = y

 

We know that the two angles are equal each other. Set up equations that represents this.

 

x + y = 90          defines the total angles.

 

2x = 3y  -->  2x - 3y = 0        defines the equality of the angles.

 

 

We have a system of equations.

 

x + y = 90                eq1

2x - 3y = 0               eq2

 

 

Substitute eq1 into eq2.   We can get eq2 in terms of x.

 

2x - 3(90 - x) = 0

 

Solve for x.

 

 

2x - 270 + 3x = 0

 

5x - 270 = 0

 

5x = 270

 

 x = 54

 

 

Substitute this value of x into eq1 to solve for y.

 

y = 90 - x

y = 90 - 54

y = 36

 

 

The angles are 36 and 54