The measure of an angle is 20 less than 3 times its supplement. Write this in an equation.
Two angles form a supplementary pair when the sum of their measures is 180 degrees.
Let x be the measure of the first angle.
Then the measure of the second angle will be 180-x since x + (180-x) = 180.
We know that the measure of the smaller angle is 20 less than 3 times its supplement.
[the measure of the first angle] = 3 * [the measure of the second angle] - 20
An equation representing this relationship is:
x = 3*(180-x) - 20
Solving for x, we have
x = 540 - 3x -20
x = 520 - 3x
4x = 520
x = 130
The first angle has a measure of 130 degrees. The second angle is its supplement so it has a
measure or 180-130=50 degrees.
We need to check that these measures satisfy all the criteria of the problem.
3 times the second angle is 3*50=150, and 130 is 20 less than 150. Check!
Feel free to email me if you have questions about this solution.