Math Geom Quiz Review 8 Answer Key

8.1-8.4 Quiz Review Geometry CP Find the sum of the measures of the interior angles of the indicated convex polygon. 21-gon: (21-2)180 = 3420° 35-gon: (35-2)180 = 5940° 50-gon: (50-2)180 = 8640° The sum of the measures of the interior angles of a convex polygon is given. Classify the polygon by the number of sides. 1440: (n-2)180 = 1440, n = 10 3780: (n-2)180 = 3780, n = 23 8820: (n-2)180 = 8820, n = 51 Find the value of x. 217 + 105 + x = 360, x = 38 824 + 32x = 1080, x = 8 7x + 248 = 360, x = 16 10. What is the measure of each interior angle of a regular octagon? (8-2)180 / 8 = 135° Use the diagram of parallelogram MNOP at the right to complete each statement. MN = PO MN || PO ON || PM ∠MPO ≅ ∠ONM PQ ≅ ON OM ≅ OQ ∠MON ≅ ∠POQ ∠NPO ≅ ∠PNM Find the value of each variable in the parallelogram. 19. 10d - 27 = 6d + 9 4d = 36 d = 9 4c + 5 = 7c - 13 18 = 3c c = 6 20. 9m + 21 = 15m - 21 42 = 6m m = 7 3n + 38 = 11n + 14 24 = 8n n = 3 21. 8t - 30 = 4t + 6 4t = 36 t = 9 9v - 13 = 2t + 5 9v - 13 = 23 9v = 36 v = 4 22. 3p + 2 = 7p - 24 26 = 4p p = 6.5 23. 5g + 11 = 3g + 15 2g = 4 g = 2 6p - 10 = 3p + 2 3p = 12 p = 4 24. 6g + 14 = 4g + 21 2g = 7 g = 3.5 9h - 4 + 6(g - 1) = 180 9h - 4 + 6(2.5) = 180 9h = 147 h = 16.33 Find the value of the variables for the following parallelograms. 25. x² + 11x = 180 x² + 11x - 180 = 0 (x + 20)(x - 9) = 0 x = -20 or x = 9 Since x cannot be negative, x = 9 y = 11x = 11(9) = 99 26. 8x + 8y = 24 x + 5y = 11 Multiplying the second equation by -8: -8x - 40y = -88 Adding the two equations: -32y = -64 y = 2 Substituting y = 2 into the second equation: x + 5(2) = 11 x = 1 For 27-28, find the PERIMETER of the parallelograms. 27. x² - 8x + 12 = 0 (x - 6)(x - 2) = 0 x = 6 or x = 2 Perimeter: 38 or 118 28. x² - 3x + 18 = 0 (x - 6)(x + 3) = 0 x = 6 or x = -3 (not possible for side length) Side length: 9 or 36 Perimeter: 36 or 144 For what value of x is the quadrilateral a parallelogram? 5x + 9 = 3x + 1 2x = -8 x = -4 8x + 19 + 21x - 13 = 180 29x + 6 = 180 29x = 174 x = 6 6x - 11 = 9x - 53 42 = 3x 14 = x The vertices of quadrilateral ABCD are given. Draw ABCD in a coordinate plane and verify that ABCD is a parallelogram. Include a short conclusion to explain your work. A(-2, 3), B(0, 5), C(6, 5), D(4, 3) Slopes: AB = 1, BC = 0, CD = -1, DA = 0 Since opposite sides have equal slopes, ABCD is a parallelogram. A(-3, -4), B(-1, 2), C(7, 0), D(5, -6) Slopes: AB = 3, BC = -1/4, CD = 3, DA = -1/4 Since opposite sides have equal slopes, ABCD is a parallelogram. Decide whether the statement is true or false. Circle either true or false. If a quadrilateral is a rectangle, then it is a parallelogram. True If a quadrilateral is a parallelogram, then it is a rhombus. False (Could be a rectangle) If a quadrilateral is a square, then it is a rhombus. True If a quadrilateral is a rectangle, then it is a rhombus. False (Could be a rectangle)