1) The sum of the interior angles of a quadrilateral is 360°. For trapezoid UVW, the angles are U, V, W, and the angle at U is 56°. Since UV is parallel to W, the consecutive angles on the same side of the transversal are supplementary. So, angle U + angle V = 180°. Therefore, angle V = 180° - 56° = 124°.
2) In trapezoid ABCD, angle C is 105°. Since AB is parallel to CD, the consecutive angles on the same side of the transversal are supplementary. So, angle C + angle D = 180°. Therefore, angle D = 180° - 105° = 75°.
3) In trapezoid MNJK, angle J is 79°. Since MN is parallel to JK, the consecutive angles on the same side of the transversal are supplementary. So, angle J + angle K = 180°. Therefore, angle K = 180° - 79° = 101°.
4) In trapezoid EFGH, angle G is 90°. Since EF is parallel to GH, the consecutive angles on the same side of the transversal are supplementary. So, angle G + angle H = 180°. Therefore, angle H = 180° - 90° = 90°.
5) The length of the midsegment of a trapezoid is the average of the lengths of the two bases. The bases are 8 and 12. So, the midsegment = (8 + 12) / 2 = 20 / 2 = 10.
6) The length of the midsegment of a trapezoid is the average of the lengths of the two bases. The bases are 11 and 17. So, the midsegment = (11 + 17) / 2 = 28 / 2 = 14.
7) The length of the midsegment of a trapezoid is the average of the lengths of the two bases. The bases are 34.6 and 10.6. So, the midsegment = (34.6 + 10.6) / 2 = 45.2 / 2 = 22.6.
8) The length of the midsegment of a trapezoid is the average of the lengths of the two bases. The bases are 30.6 and 11. So, the midsegment = (30.6 + 11) / 2 = 41.6 / 2 = 20.8.
9) The length of the midsegment of a trapezoid is the average of the lengths of the two bases. The bases are 27 and 17. So, the midsegment = (27 + 17) / 2 = 44 / 2 = 22. Therefore, x + 10 = 22, so x = 12.
10) The length of the midsegment of a trapezoid is the average of the lengths of the two bases. The bases are 44 and 22. So, the midsegment = (44 + 22) / 2 = 66 / 2 = 33. Therefore, 10x - 7 = 33, so 10x = 40, and x = 4.
Parent Tip: Review the logic above to help your child master the concept of trapezoids worksheet answers.
