Two angles are supplementary. One angle is 4 degree less than 3 times the other. Find the measures of the angles.
Supplementary angles: two angles whose measures total 180 deg
x = 1st angle
3x - 4 = 2nd angle
x + 3x - 4 = 180
solve for x to find the angles
x=46
To solve this problem, let's represent the two angles by variables.
Let's call one angle x and the other angle y.
According to the problem, the two angles are supplementary, which means the sum of their measures is 180 degrees. Therefore, we can write the equation:
x + y = 180
It is also given that one angle is 4 degrees less than 3 times the other. This can be expressed as an equation:
x = 3y - 4
Now we have a system of two equations that we can solve to find the values of x and y.
To solve this system, we will use the method of substitution. We will start by solving the second equation for x in terms of y.
x = 3y - 4
Now substitute this expression for x in the first equation:
(3y - 4) + y = 180
Combine like terms:
4y - 4 = 180
Add 4 to both sides:
4y = 184
Now divide both sides by 4:
y = 46
Now substitute the value of y back into either of the original equations to find x:
x = 3y - 4
x = 3(46) - 4
x = 138 - 4
x = 134
Therefore, the measures of the angles are x = 134 degrees and y = 46 degrees.