Question

Vertical lines m and n are intersected by lines k and j. At the intersection of lines m and k, the bottom right angle is (x minus 30) degrees. At the intersection of m and j, the uppercase right angle is y. At the intersection of lines k and n, the bottom left angle is (x + 50) degrees.
Find the values of x and y that make k || j and

m || n.




x =? °


y = ?°

Answer 1

Using the same-side interior angles theorem, the values of x and y are:

x = 80

y = 130

What is the Same-side Interior Angles Theorem?

The same-side interior angles theorem states that two interior angles on same side of a transversal are supplementary.

(x - 30) and (x + 50) are same-side interior angles, therefore:

(x - 30) + (x + 50) = 180

Solve for x

x - 30 + x + 50 = 180

2x + 20 = 180

2x = 180 - 20

2x = 160

x = 160/2

x = 80

(x - 30) + y = 180

Plug in the value of x

(80 - 30) + y = 180

50 + y = 180

y = 180 - 50

y = 130

Learn more about the same-side interior angles theorem on:

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