Question

two complementary angles are such that two times the measures of one is equal to three times measure of the other. find the measures of the large angle

Answer 1

Complementary angles of the angles whose sum is equal to 90 degree

Let the measure of the angle be 2x and 3x

So 2X + 3 x is equal to 90

5x=90

X=90÷5

X=18

So angles are.

2×x=2×18=36°

3×x=3×18=54°

So the measure of the larger angle is 54 degree hope it helps please regard this answer as the brainliest

Best regards

Answer 2

Complementary angles add up to 90 degrees.  Assign variable for the angles.

 

 

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.

 

The larger angle is 54 degrees.