Given: m∠1 = 62° and lines t and l intersect Prove: m∠4 = 62°

Answer 1

I presume that angles 1 and 4 are vertical angles at the intersection of line l with transverse t. So let either of the two angles that fall between them be angle 2. then since angles 1 and 2 form a straight line, the sum of their measures = 180 degrees. Then the measure of angle 2 = 180 - 62 = 118 degrees. Now since angles 2 and 4 form another straight line, the sum of their measures = 180 degrees also. Then the measure of angle 4 = 180 - 118 = 62 degrees. QED