set up a system to solve. Two angles are supplementary. Twice one angle is equal to the other anlge minus 36. Find both angles.
The answer is x=48 and y=132 but how did they get this answer?
two angles are supplementary if they add to 180. So, if one angle is x, the other is (180-x), and you have
2x = (180-x)-36
2x = 133-x
3x = 144
x = 48
To solve this problem, we need to set up a system of equations based on the given information and then solve it. Let's denote the measure of one angle as x and the other angle as y.
1. The first piece of information states that the two angles are supplementary. This means that their measures add up to 180 degrees, so we can write the equation:
x + y = 180
2. The second piece of information states that "Twice one angle is equal to the other angle minus 36." Translating this into an equation, we have:
2x = y - 36
Now we have a system of two equations with two variables. To find the values of x and y, we can solve this system using substitution or elimination method.
Let's proceed with the substitution method:
1. Rearrange the first equation to express x in terms of y:
x = 180 - y
2. Substitute this value of x into the second equation:
2(180 - y) = y - 36
3. Simplify the equation:
360 - 2y = y - 36
4. Solve for y:
-2y - y = -36 - 360
-3y = -396
y = (-396) / (-3)
y = 132
5. Substitute the value of y back into the first equation to find x:
x + 132 = 180
x = 180 - 132
x = 48
So, the two angles are 48 degrees and 132 degrees.