Question 1041055
{{{drawing(300,300,-15,15,-15,15,
line(-16,-5,16,-5),
line(16,5,-16,5),
line(-10,-15,10,15),
locate(-7,-4.9,38^o),locate(-3,-5.2,7),
locate(1.5,4.9,2),locate(3.8,4.9,5),
locate(4.5,7,4),locate(2,7,3),
locate(-4.4,-3,1),locate(-2.1,-3,6),
locate914,-5,M),locate(14,5,L)
)}}}  Lines L and M are parallel lines,
intersected by the slanted line that we call a transversal.
The angle labeled as {{{2}}} is what you would get if you move up the angle measuring {{{38^o}}} sliding it along the slanted line.
So the angle labeled {{{2}}} also  measures {{{38^o}}}
Those two angles, on the same position are called corresponding angles,
and have the same measure.
The angles labeled {{{1}}} and {{{3}}} are another pair of corresponding angles.
We can find their measure , because they are supplementary to the angles labeled {{{38^o}}} and {{{2}}} respectively.
So the measure of the angles labeled {{{1}}} and {{{3}}} is
{{{180^o-38^o=142^o}}} .
The other angles measure either {{{38^o}}} or 142^o}}} .
The angle labeled {{{4}}} is supplementary to the angle labeled {{{3}}} ,
just like angle {{{2}}} is. So, angles {{{2}}} and {{{4}}} have the same measure, {{{38^o}}} ,
because they are both supplementary to angle 3,
Pairs of angles like {{{2}}} and {{{4}}}, made from the same two lines,
but sharing only their vertices, are called vertical angles.
Angle {{{6}}} measures {{{38^o}}} because it forms a pair of vertical angles with the angle labeled {{{38^o}}} .
By the same reasoning, angles {{{3}}} and {{{5}}} , forming a vertical pair,
have the same measure, {{{142^o}}} , as we had found for angle {{{3}}} .
Similarly, angle {{{7}}} , also measures {{{142^o}}} ,
like its vertical angle, angle {{{1}}} .