Question 618363
{{{drawing(300,300,-10,10,-10,10,
arrow(0,0,8.356,9.959),arrow(0,0,-8.356,-9.959),
arrow(0,-4,-10,-4),arrow(0,-4,10,-4),
arrow(0,4,-10,4),arrow(0,4,10,4),
locate(2.7,4.9,1),locate(4.2,4.9,2),
locate(2.1,4,4),locate(3.6,4,3),
locate(-4.3,-3.1,5),locate(-2.6,-3.1,6),
locate(-4.7,-4,8),locate(-3.2,-4,7)
)}}} Angles 2, 4, 6, and 8 measure {{{50^o}}}, the other angles measure
{{{180^o-50^o=130^o}}}
 
THE REASONS (one of many ways to justify the conclusions):
I made the drawing so that the measure of angle 2 would be {{{50^o}}}.
As for the other angles, we apply what was learned in geometry class:
Angles opposed "tip to tip", like the pair 2 and 4, and the pair 6 and 8, are called vertical and are congruent (same measure). So angle 4 measures {{{50^o}}} because it is vertical to angle 2.
Angles in between the parallel lines, but on different sides of the transversal, like the pair of 4 and 6, are called alternate interior, and are also congruent. So angle 6 measures {{{50^o}}} because it is alternate interior to angle 4.
And angle 8, vertical to 6, also measures {{{50^o}}}.
Each of the other angles is supplementary to a {{{50^o}}} angle, and must measure {{{130^o}}} because a pair of supplementary angles must add to {{{180^o}}}.
NOTE:
There are different ways to explain the same conclusions. For example, you could say that angle 1 is suplementary to angle 2, or that it is supplementary to angle 4; it works one way or the other. You pick one, no need to say it both ways. Something similar happens for angles 3, 5, and 7.