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.