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Find the value of x and y

Find the value of x and y-example-1
User Krzysztof Majewski
by
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1 Answer

23 votes
23 votes

Answer:

x = 10 and y = 15

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!

User Yshk
by
2.7k points