Question

1.Parallelogram ACFD is split in two parts so that ABED and FEBC are congruent isosceles trapezoids. What are the measures of all the angles of trapezoid FEBC if angle D is 48°?
I know that Angle C is 48 degrees
I know that Angle F is 132 degrees
What is < CBE equal to and why?
What is < FEB equal to and why?

Answer 1

Refer to the diagram shown below.

Because ACFD is a parallelogram, its opposite angles are equal. Therefore
x = m∠ACF = m∠BCF = 48°  
Similarly,
y = m∠CAD = m∠CFD 

The sum of the angles inside a parallelogram is 360°. Therefore
48° + x + y + y = 360°
Because x = 48°,
48° + 48° + 2y = 360°
2y = 360° - 96° = 264°
y = 132°

Because ABED and FEBC are congruent, therefore
y = m∠DAB = m∠CFE = 132°
x = m∠ADE = m∠FCB = 48°

Because FEBC is a parallelogram, the opposite angles are equal. Therefore
m∠CBE = m∠CFE = y = 132°
m∠BCF = m∠BEF = x = 48°

Answer:
The measures of all angles of trapezoid FEBC are
m∠BCF = 48°
m∠BEF = 48°
m∠CBE = 132°
m∠CFE = 132°