# The measure of the complement of an angle is three times the measure of the angle. What is the measure of each angle?

Question
The measure of the complement of an angle is three times the measure of the angle. What is the measure of each angle?

2020-12-01
If x is the measure of an angle, then 90−x is the measure of its complement because complementary angles have an angle sum of 90°.
The measure of the complement of an angle is three times the measure of the angle so we write:
90−x=3(x)
Solve for x:
90−x=3x
90=4x
22.5=x
So, the measures of the angles are:
22.5° and 67.5°

### Relevant Questions

The measure of the supplement of an angle is $$\displaystyle{40}^{{\circ}}$$ more than three times the measure of the original angle. Find the measure of the angles. Instructions: Use the statement: " Let the original angle be x " to begin modeling the working of this question.

a) Write algebraic expression in terms of x for the following:

I) $$40^{\circ}$$ more than three times the measure of the original angle

II) The measure of the Supplement angle in terms of the original angle, x

b) Write an algebraic equation in x equating I) and II) in a)

c) Hence solve the algebraic equation in

b) and find the measure of the angles.

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