In response: a) M5 = 40º
b) M2 equals 140º
c) The supplementary angles M2 and M5
d) The interior angles M2 and M5 are the same side.
e) A||B .
The provided statements revolve around angle measurements and relationships within the context of parallel lines and transversals.
Let's elaborate on each statement:
a) M5 = 40º:
This statement asserts that the angle measurement of angle M5 is 40º.
b) M2 equals 140º:
This statement declares that angle M2 has a measurement of 140º.
c) The supplementary angles M2 and M5:
The term "supplementary" implies that the angles add up to 180º. This statement suggests that angles M2 and M5 form a pair of supplementary angles.
d) The interior angles M2 and M5 are the same side:
This statement appears to contain a typographical error, as it seems to be similar to the previous statement regarding supplementary angles.
The correct term might be "same-side interior angles," which typically refer to angles located on the same side of a transversal that intersects two parallel lines.
e) A||B:
This statement makes a conclusion about the parallelism of lines A and B.
It uses the information about the supplementary angles M2 and M5 being on the same side of a straight line that intersects two parallel lines to assert that lines A and B are parallel.
The reasoning involves the fact that the sum of same-side interior angles is always 180º, which is a characteristic of parallel lines when cut by a transversal.
The statements provide information about specific angle measurements and use the concept of supplementary angles and same-side interior angles to draw conclusions about the parallel relationship between lines A and B.
The reasoning demonstrates an understanding of geometric principles related to angles and parallel lines.