Answer:
x = 20°
y = 40°
Explanation:
Angles on the same line add up to 180 degrees. We can see angles 2x, 3y, and x are on the same line. This means:
2x + 3y + x = 180 ⇒ 3x + 3y = 180 divide by 3 ⇒ x + y = 60
There is another line that contains the angles 3y, x, and y. This gives us our second equation:
3y + x + y = 180 ⇒ x + 4y = 180
We have two equations, or a system of linear equations. We can solve this using multiple different methods. However, let's use elimination. We need to "eliminate" the x variable. To do this, let's subtract the first equation from the second equation:
x + 4y - (x + y) = 180 - 60 ⇒ x + 4y - x- y = 120 ⇒ 3y = 120
Dividing both sides by 3, we get:
y = 40
Substituting this value back into the first equation, we get:
x + y = 60 ⇒ x + 40 = 60 ⇒ x = 20