Question

Two complementary angles are such that twice the measure of the one is equal to three times the measure of the other . what is the value of larger of two angles ?​

Answer 1

Answer:

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.

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The larger angle is 54 degrees