The Legs - The two non parallel lines are the legs.

Diagram 1

Diagram 2

Properties

Property #1) The angles on the same side of a leg are called adjacent angles and are supplementary( more )

Property #2)Area of a Trapezoid = $$ Area = height \cdot \left( \frac{ \text{sum bases} }{ 2 } \right) $$ ( more )

Property #3) Trapezoids have a midsegment which connects the mipoints of the legs( more )

Adjacent Angles of Trapezoid

The angles on the same side of a leg are called adjacent angles such as $$\angle A $$ and $$ \angle D $$ are supplementary. For the same reason, $$ \angle B $$ and $$ \angle C $$ are supplementary.

Use adjacent angles theorem to calculate m $$ \angle MLO $$.

$$ \angle MLO = 180-124 = 56° $$

Problem 3

Find the value of x in the trapezoid below, then determine the measure of angles$$ \angle WXY $$ and $$ \angle XYZ $$.

Problem 4

What is wrong with trapezoid LMNO pictured below? (Explain why LMNO cannot be a trapezoid based on the information provided).

If LMNO is a trapezoid and its basesLO and MN are parallel then, $$ \angle MNO $$ and $$ \angle NOL $$ which must be supplementary however, the sum of these angles is not 180 111 + 68 ≠ 180.