1. The legs of isosceles trapezoid ABCD are AB and CD.
2. The bases of isosceles trapezoid ABCD are AD and BC.
3. The base angles of isosceles trapezoid ABCD are ∠A and ∠B.
4. Since isosceles trapezoid ABCD is isosceles, then ∠A = ∠B. Therefore, if m∠A = 70, then m∠B = 70 degrees as well.
5. Since isosceles trapezoid ABCD is isosceles, then ∠C = ∠D. Therefore, if m∠D = 105, then m∠C = 105 degrees as well.
6. Since isosceles trapezoid ABCD is isosceles, then m∠A = m∠B and m∠C = m∠D. Therefore, m∠A + m∠B + m∠C + m∠D = 360 degrees. We can substitute the given values and the expression for m∠B to get: 70 + (2x-6) + 82 + 105 = 360. Solving for x, we get x = 59.
7. We can use the fact that the opposite angles of isosceles trapezoid ABCD are supplementary. Therefore, m∠C + m∠D = 180. Substituting the given values, we get: 20 + m∠DH = 180. Solving for m∠DH, we get m∠DH = 160 degrees.
8. We can use the fact that the diagonals of an isosceles trapezoid are congruent. Therefore, AR = BC. Since AC = 56, then AR = BC = (56 - DR). Solving for DR, we get DR = 28 cm.
Answers & Comments
Answer:
1. The legs of isosceles trapezoid ABCD are AB and CD.
2. The bases of isosceles trapezoid ABCD are AD and BC.
3. The base angles of isosceles trapezoid ABCD are ∠A and ∠B.
4. Since isosceles trapezoid ABCD is isosceles, then ∠A = ∠B. Therefore, if m∠A = 70, then m∠B = 70 degrees as well.
5. Since isosceles trapezoid ABCD is isosceles, then ∠C = ∠D. Therefore, if m∠D = 105, then m∠C = 105 degrees as well.
6. Since isosceles trapezoid ABCD is isosceles, then m∠A = m∠B and m∠C = m∠D. Therefore, m∠A + m∠B + m∠C + m∠D = 360 degrees. We can substitute the given values and the expression for m∠B to get: 70 + (2x-6) + 82 + 105 = 360. Solving for x, we get x = 59.
7. We can use the fact that the opposite angles of isosceles trapezoid ABCD are supplementary. Therefore, m∠C + m∠D = 180. Substituting the given values, we get: 20 + m∠DH = 180. Solving for m∠DH, we get m∠DH = 160 degrees.
8. We can use the fact that the diagonals of an isosceles trapezoid are congruent. Therefore, AR = BC. Since AC = 56, then AR = BC = (56 - DR). Solving for DR, we get DR = 28 cm.