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Lines and Angles

Short Answer Type

41. In figure, l || m, show that ∠1 + ∠2 - ∠3 = 180°.

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42. In figure, AB || CD and CD || EF. Also EA ⊥ AB. If ∠BEF = 40°, then find x, y, z.

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43. In the figure below, l₁ || l₂ and a₁ || a₂. Find the value of x.

∠1 = 4x - 15 | Corresponding angles
2x = ∠1 = 4x - 15
| Corresponding angles

$rightwards double arrow space space space straight X equals 7 1 half$

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Long Answer Type

44. Two parallel lines are intersected by a transversal. Then, prove that the bisectors of two pairs of interior angles enclose a rectangle.

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Short Answer Type

45. In the figure, if PQ || RS, ∠MXQ = 135° and ∠MYR = 40°, find ∠XMY.

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46. If a transversal intersects two lines such that the bisectors of a pair of corresponding angles are parallel, then prove that the two lines are parallel.

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47. In the figure, AB || CD and CD || EF. Also EA ⊥ AB. If ∠BEF = 55°, find the values of x, y and z.

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48. In figure, if AB || CD then find the value of x.

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49. AB and CD are the bisectors of the two alternate interior angles formed by the intersection of a transversal 't' with parallel lines l and m. Show that AB || CD.