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

x = 80°
y = 130°

Reason: For k crossing m and n, the two given angles are same-side interior, so (x−30)+(x+50)=180 → 2x+20=180 → x=80.
If k || j, the bottom-right angle at m for k (x−30 = 50°) equals the bottom-right angle at m for j, which is supplementary to the given upper-right y: 50 = 180 − y → y = 130.