Question

Two complementary angles are such that two times the measure of one is equal to three times the measure of the other. Find the measures of the larger angle

Answer 1

Answer: 54°

Step-by-step explanation:

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.

Answer 2

Answer:

Step-by-step explanation: