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5. If the measure of each interior angle of a regular polygon is 108 , find the measure of each exterior angle. (A) 18∘ (C) 108∘ (B) 90∘ (D) 72∘ 6. Which of the following is a property of all parallelograms? (A) Each pair of opposite angles is congruent. (B) Only one pair of opposite angles is congruent. (C) Each pair of opposite angles is supplementary. (D) There are four right angles. 7. For rhombus GHJK, find m∠1. (A) 22∘ (B) 44∘ (C) 68∘ (D) 90∘ 8. Judith built a fence to surround her property. On a coordinate plane, the four cormers of the fence are located at (−16,1),(−6,5),(4,1), and (−6,−3). Which of the following most accurately describes the shape of Judith's fence? (A) square (B) rectangle (C) rhombus (D) trapezoid 9. Parallelogram ABCD has vertices A(8,2),B(6,−4), and C(−5,−4). Find the coordinates of D. (A) D(−5,2) (B) D(−3,2) (C) D(−2,2) (D) D(−4,8) 10. - For parallelogram ABCD, find m∠1. (A) 60∘ (B) 54∘ (C) 36∘ (D) 18∘ 1107 American School-Lansing, IL
Student Name Student Number 11. For kite PQRS, find m∠S. (A) 248∘ (B) 68∘ (C) 112∘ (D) 124∘ 12. ABCD is a rectangle. If AC=5x+2 and BD=x+22, find the value of x. (A) 5 (B) 6 (C) 11 (D) 26 13. Find the sum of the measures of the exterior angles of a convex 21-gon. (A) 21∘ (B) 180∘ (C) 360∘ (D) 3420∘ 14. For parallelogram ABCD, find the value of x. (A) 4 (B) 10 (C) 16 (D) 21.5 15. The length of one base of a trapezoid is 44 , the median is 36 , and the other base is 2x+10. Find the value of x. (A) 9 (B) 17 (C) 21 (D) 40
To receive full credit for the following questions, show as much work as possible. 16. Determine whether each quadrilateral is a parallelogram. Justify your answer using a theorem. 17. For trapezoid HJKL, T and S are midpoints of the legs. If HJ=14 and LK=42, find TS.
18. Complete the proof below. Given: RSTV is a rectangle and U is the midpoint of VT. Prove: △RUV≅△SUT Proof: 19. Find the sum of the interior angle measures. Then, find the measure of each interior angle.
20. Determine whether the quadrilateral is a parallelogram. Justify your answer. 21. ABCD is a parallelogram and AC≅BD.Determine whether ABCD is a rectangle. Justify your answer. 22. Find the measure of ∠D. Justify your answer. 23. Find the value of each variable in the following parallelogram.
If DK=8, find KL. Justify your answer. A. If DK=8, find KL. Justify your answer. B. If m∠SKAL=2x−8, find x. Justify your answer. C. If DM=5y+2 and DK=3y+6, find KL. Justify your answer. 25. Quadrilateral ABCD is a rectangle. If m∠BDC=7x+1 and m∠ADB=9x−7, find m∠BDC.
25. Use the given vertices to determine whether the figure is a parallelogram. Justify your answer with the methods indicated. S(−2,1),R(1,3),T(2,0),Z(−1,−2); Distance and Slope Formulas