Answer:
x = 10 and y = 15
Step-by-step explanation:
The arrows on lines AB and CD indicate that they are parallel. This means that we have to look for Z-angles (I don't know if they are called the same where you're from but I hope you recognise the term). This means that ∠ABC = ∠BCD
5x - 20° = x + 20°
4x = 40°
x = 10°, which gives us the first answer.
The angle formed by points ACE (a straight line) is 180 degrees. Lets refer to this as angle ACE. We also know this angle consists of angle ACB, BCD and DCE. This gives us the following equation:
angle ACE = angle ACB + x + 20° + y + 20° = 180°
angle ACB + x + y + 40° = 180°
angle ACB = -x - y + 140°
Inserting the x we found earlier this gives
∠ACB = - y + 130°
Now we can find a second equation to describe ACB by looking at the triangle it is inside. The angles in a triangle always add up to 180°, giving the following expression:
4y - 25° + 5x - 20° + ∠ACB = 180°
Substituting x again gives
4y - 25° + 50° - 20° + ACB = 180°
ACB = 180 - 4y - 5° = 175° -4y
Combining the two expressions for ACB gives the final equation to solve:
175° - 4y = -y + 130°
-3y = -45
y = 15
If you have any questions still feel free to reach out!
