If <10 and <15 are congruent, which lines are parallel? A. lines b and c B. lines c and d C. lines a and b D. No lines are parallel. - Refer to second picture. Given the information in the diagram, determine if M ll N If so, give the theorem or postulate used to support your conclusion. A. yes; converse of the consecutive interior angles theorem B. yes; converse of the alternate interior angles theorem C. yes; converse of the corresponding angles postulate D. no

Problem 1

Explanation: Circle or highlight the angles 10 and 15. They are alternate interior angles with line d being the transversal cut. It might help to try to erase line c to picture the transversal line d better. With d as the transversal, and angles 10 and 15 congruent, this must mean lines a and b are parallel by the alternate interior angle theorem converse.

Problem 2

Explanation: The angles at the top are 32 degrees, 90 degrees, and x degrees which is the missing unmarked angle at the top (all three angles are below line m). The three angles must add to 180 to form a straight angle

32+90+x = 180

x+122 = 180

x = 180-122

x = 58

The missing angle is 58 degrees. This is very close to 57 degrees at the bottom. Though we do not have an exact match. This means lines m and n are not parallel. The alternate interior angles must be congruent for m and n to be parallel, as stated earlier in problem 1.