Here are some useful theorems and definitions for these problems:
1. Alternate interior angle theorem: when you have 2 parallel lines with a transversal passing through both of them, the 2 alternate interior angles such as <3, <1 are equal.
2.Alternate exterior angles theorem: when you have 2 parallel lines with a transversal passing through both of them, the 2 alternate exterior angles such as <8 and <6 are equal
3. Corresponding angles theorem: when you have 2 parallel lines with a transversal passing through both of them, the 2 corresponding angles such as <8 and <1 are equal.
4.Same-side interior angles theorem: when you have 2 parallel lines with a transversal passing through both of them, the 2 angles on the same side interior, such as <4 and <1, adds up to 180 degrees.
5. Vertical angles theorem: vertical angles, angles that are opposite each other and formed by two intersecting straight lines, are congruent (or equal)
6. Supplementary angles: when 2 angles combine to make a line these 2 angles adds up to 180 degrees and are called supplementary angles.
Now apply one or more of these theorems to each of the problems to find out the answer!
1. Same side interior angle theorem: 56 degrees.
2. Same side interior angle theorem: 132 degrees.
3. Alt. Interior angles theorem: 55 degrees.
4. Alt. exterior angles theorem: 120 degrees
5. <7 --> <2 corresponding angles theorem: <2=50.5 degrees
<2 --> <6 supplementary angles: <6=129.5 degrees
6.Same side interior angles theorem: 61.3 degrees
