dont understand this geometry problem?

Question

my teacher gave me like 10 problems like these and i have no idea what to do!?


http://s1377.photobucket.com/user/breanaramos17/media/geodiagram_zps452fcc3f.gif.html?filters[user]=140775450&filters[recent]=1&sort=1&o=0

in the puzzle below…

lines line a and line b are parallel.
lines line c and line d are parallel.
line line d is perpendicular to line line e.
Find the measures of angles 1–15.

Answer 1

Line a and line b are parallel.

Line c and line d are parallel.

Line d is perpendicular to line e.

Find the measures of angles 1–15.

Angles 1 to 15:



∠1 = ∠12 = 130°

∠9 = ∠14 = 40°

∠10 = ∠11 = 50°

∠13 = ∠15 = 140°

∠4 = 30°

∠6 = 50°

∠2 = 50°

∠5 = 70°

∠3 = 50°

∠7 = 60°

∠8 = 40°

Answer 2

1) When two lines intersect the angles opposite of each other are equal.

2) All the angles on one side of a line add up to 180 degrees.

3) All angles inside of a triangle add up to 180 degrees.

4) Perpendicular means 90 degrees. Also all angles inside of one of the 4 quadrants add up to 90 degrees.

5) If two lines are parallel and a line crosses one of them at a certain angle, the angle where it crosses the other line is the same angle.



From (5) and (4) and the 60 degree angle you can find angle 4 pretty easily. From (2) you can find angle 6 pretty easily. From (5) and (1) you can find 1, 10, 11 and 12. From 11 and (3) you can find 9. From 9, (1) and (2) you get 13, 14 and 15. Etc. (all the remaining angles use the same 5 rules).

Answer 3

ang 4 = 90 - 60 = 30 (c,e perpendicular)

ang 6 = 180 -130 = 50 (on a straight line)

ang 2 = ang 6 = 50

ang 14 = 180 - 90 - ang 6 = 40 (180 degrees in a triangle)

ang 9 = ang 14 = 40

ang 8 = ang 9

ang 13 = 180 - ang 14 = 140 (on a straight line)

ang 15 = ang 13

ang 11 = 180 - 90 - ang 9 = 50 (180 degrees in a triangle)

ang 10 = ang 11 = 50

ang 1 = 180 - ang 11 = 130 (on a straight line)

ang 12 = ang 1 = 130

ang 3 = ang 10 = 50

ang 7 = 180 - 90 - 30 = 60 (180 degrees in triangle, and angle at PDH = ang 6)

ang 5 = 180 - ang 7 - ang 3 = 180 - 60 - 50 = 70 ((180 degrees in triangle, and other angles follow from known angles.)

Answer 4

I forget what they're called, but you could start by looking at pairs of angles like SRQ and angle 1. Those are two angles formed by the same straight line as it cuts two parallel lines, and they're the same. So angle 1 is also 130 degrees.



Then you could look for complementary angles. Angles 1 and 11 add up to 180.



And you could look for triangles where you know two of the angles and you know the three angles have to add up to 180 degrees.