The angles for the larger base of the trapezoid are 75 degrees and 43 degrees. Find the angles at my base.

Given:
trapezoid ABCE,
ВС and АЕ – bases,
angle BAE = 75 degrees,
angle CEA = 43 degrees.
Find the degree measures of angles with a smaller base, that is, the angle ABC and the angle BCE -?
Solution:
Consider the trapezoid ABCE.
In it, the bases of BC and AE are parallel. Then angle BAE and angle ABC are internal one-sided angles for parallel straight lines BC and AE and secant AB, then
angle BAE + angle ABC = 180 degrees;
angle ABC = 180 – angle BAE;
angle ABC = 180 – 75;
angle ABC = 105 degrees.
Angle BCE and angle CEA are internal one-sided angles for parallel straight lines BC and AE and secant CE, then
angle BCE + angle CEA = 180 degrees;
angle BCE = 180 – angle BAE;
angle BCE = 180 – 43;
angle BCE = 137 degrees.
Answer: 105 degrees; 137 degrees.