1. **Find m\angle? in the trapezoid with one angle marked 112°** Given that trapezoid has one angle measuring 112° and the adjacent angle on the same base is m\angle?. Since these two angles are consecutive interior angles between parallel lines, they are supplementary. Formula: \n\angle? + 112^\circ = 180^\circ Step 1: Write the equation $$m\angle? + 112 = 180$$ Step 2: Subtract 112 from both sides $$m\angle? = 180 - 112$$ Step 3: Calculate $$m\angle? = 68^\circ$$ 2. **Find PQ, the midsegment of trapezoid ABCD where AB = 14 and DC = 22** Formula for midsegment of trapezoid: $$PQ = \frac{AB + DC}{2}$$ Step 1: Substitute values $$PQ = \frac{14 + 22}{2}$$ Step 2: Simplify numerator $$PQ = \frac{36}{2}$$ Step 3: Simplify fraction $$PQ = 18$$ 3. **Vocabulary matching** - A __________ is a quadrilateral with both pairs of opposite sides parallel. - Answer: parallelogram - A __________ is a parallelogram with all four sides congruent. It may or may not have four right angles. - Answer: rhombus - A __________ is a parallelogram with all four sides and all four angles congruent. - Answer: square - A __________ is a convex quadrilateral with exactly two distinct pairs of adjacent congruent sides. - Answer: kite 4. **Find m\angle D in parallelogram DEFG with angle F = 106°** Opposite angles in a parallelogram are equal, and adjacent angles are supplementary. Step 1: Adjacent angles sum to 180° $$m\angle D + 106 = 180$$ Step 2: Solve for m\angle D $$m\angle D = 180 - 106 = 74^\circ$$ 5. **Find VY in square WXYZ where WY = 36** Diagonals of a square bisect each other, so V is midpoint of WY. Step 1: Calculate half of WY $$VY = \frac{WY}{2} = \frac{36}{2} = 18$$ 6. **Find x in rhombus PQRS where PQ = 2x + 4 and PS = 4x - 4** All sides of a rhombus are equal. Step 1: Set sides equal $$2x + 4 = 4x - 4$$ Step 2: Subtract 2x from both sides $$4 = 2x - 4$$ Step 3: Add 4 to both sides $$8 = 2x$$ Step 4: Divide both sides by 2 $$\cancel{2x} = \frac{8}{\cancel{2}}$$ $$x = 4$$