Find the smaller side of a rectangular trapezoid whose bases are 10 cm and 6 cm, and one of the corners is 45 degrees.

Given:
ABCE – rectangular trapezoid,
BC = 6 centimeters,
AE = 10 centimeters,
angle E = 45 degrees.
Find the side of AB -?
Decision:
1) Consider a rectangular trapezoid ABCE. Let’s draw the height of the CH. We get a rectangle ABCO, then BC = AO = 6 centimeters, AB = CO.
2) Consider a right-angled triangle COE. Side OE = AE – AO = 10 – 6 = 4 (centimeters). We know that the sum of the degree measures of the angles of any triangle is 180 degrees.
Then the angle AСE + angle CEO + angle EOC = 180;
angle AСE = 180 – 90 – 45;
AСE angle = 45 degrees.
Therefore, the СOE triangle is isosceles, then CO = OE = AB = 4 centimeters.
Answer: 4 centimeters.