Line KP intersects line AB at point K, and line CD at point P so that points B and D lie on the same side

Line KP intersects line AB at point K, and line CD at point P so that points B and D lie on the same side of line KP. Are lines AB and CD parallel if angle BKP = 89, angle KPD = 90?

Given: Line KP intersects line AB at point K;
line KP intersects line CD at point P;
points B and D lie on the same side of the KP;
angle BKP = 89 degrees,
angle KPD = 90 degrees.
Are lines AB and CD – parallel?
Solution: Let’s say AB and CD are parallel. Then the angle BKP and the angle KPD are one-sided angles for these lines and secant KP. The sum of the degree measures of one-sided angles with parallel lines should be equal to 180 degrees. Find the angle BKP + angle KPD = 89 + 90 = 179 degrees. Then AB and CD are not parallel.
Answer: No.



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