Question

Horizontal lines n and m are intersected by lines q and p. At the intersection of lines q and n, the uppercase right angle is angle 4. At the intersection of lines q and m, the uppercase left angle is angle 1. At the intersection of lines p and n, the bottom left angle is angle 3. At the intersection of lines p and m, the uppercase left angle is angle 2.
If angle 1 is 110°, what would the other angle measures have to be in order for m || n and
q || p?



Angle 2 =
°



Angle 3 =
°



Angle 4 =
°

Answer 1

Angle 2 = 110°

Angle 3 = 70°

Angle 4 = 70°

Reason: q || p so angle2 (upper-left at m on p) = angle1 = 110°. With m || n, the upper-right angles at n are supplements of the upper-left angles at m, so angle4 = 180° − 110° = 70°. Likewise angle3 (bottom/ lower-left on n for p) = 180° − angle2 = 70°.