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
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Answered by
205
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.
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