Question

With the given information and what you are able to determine, can you conclude that A || B?

P || Q
M<2 = 8x + 14
M<4 = 13y + 19
M<12 = 15y + 5
M<13 = 10x - 10

Answer 1

Answer:

  yes, A║B

Step-by-step explanation:

Given that P║Q, alternate exterior angles 2 and 13 are congruent. This means ...

  8x +14 = 10x -10

  24 = 2x . . . . . . . . . . subtract 8x-10

Then the measures of these angles are ...

  5(2x) -10 = 5(24) -10 = 110 . . . . measure of angles 2 and 13

__

Similarly, corresponding angles 4 and 12 are congruent. This means ...

  13y +19 = 15y +5

  14 = 2y

  7 = y

Then the measures of these angles are ...

  15(7) +5 = 110 . . . . measure of angles 4 and 12

Angles 2 and 4 are corresponding. We have demonstrated that they have the same measure, so lines A and B must be parallel.