Answer:
x=36
y=72
When a pair of parallel lines is intersected by a transversal (a line that goes through both parallel lines), angle relationships are formed.
We first observe that the angles with measures of (3x)° and (2x)° lie on the transversal and are adjacent (next to) each other. So, these two angles are a linear pair. Both angles form the angle measure of the transversal, and the measure of a line is always 180.° Therefore, both angles must have a sum of 180.° Let’s create an Algebraic equation and solve for x with this information.
The pair of angles are adjacent to each other and form the measure of the transversal, thus the angles can add to sum up to 180.
(3x)°+(2x)°=180°
We’ll temporarily remove the degree symbol so that we are working with regular values. This also removes the parenthesis:
3x+2x=180
Let’s solve for x:
1.) Combine like terms:
5x=180
2.) Use properties of equality and inverse operations to solve for x:
5x/5=180/5
x=36
Now, let’s solve for y.° The angle that measures (2x)° is congruent to the angle that measures y° because they are corresponding angles. We already know that x=36, so if we plug x into (2x),° we’ll know the angle measure of y.° Let’s form an equation:
(2x)°=y°
Plug in x=36:
[2(36)]°=y°
°72=y°
y°=72°