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ABCD is a quadrilateral in which /A= 60^...

ABCD is a quadrilateral in which `/_A= 60^(@), /_ B= 70^(@), /_ C =110^(@)` and `/_ D =120^(@)`. The number of pairs of parallel lines is `"________________"`.

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To determine the number of pairs of parallel lines in the quadrilateral ABCD, we can follow these steps: ### Step-by-Step Solution: 1. **Identify the Angles:** We have the following angles in the quadrilateral: - Angle A = 60° - Angle B = 70° - Angle C = 110° - Angle D = 120° 2. **Check for Parallel Lines:** According to the properties of parallel lines, if two angles on the same side of a transversal sum up to 180°, then the lines are parallel. 3. **Calculate the Sums of Angle Pairs:** We will check the following pairs of angles: - Pair 1: Angle A + Angle B = 60° + 70° = 130° (not parallel) - Pair 2: Angle B + Angle C = 70° + 110° = 180° (parallel) - Pair 3: Angle C + Angle D = 110° + 120° = 230° (not parallel) - Pair 4: Angle D + Angle A = 120° + 60° = 180° (parallel) 4. **Identify Parallel Lines:** From the calculations: - Angles A and B do not form a pair of parallel lines. - Angles B and C form one pair of parallel lines. - Angles C and D do not form a pair of parallel lines. - Angles D and A form another pair of parallel lines. 5. **Count the Pairs of Parallel Lines:** We found two pairs of angles that sum to 180°: - Pair 1: Angles B and C - Pair 2: Angles D and A 6. **Conclusion:** Therefore, the number of pairs of parallel lines in quadrilateral ABCD is **2**. ### Final Answer: The number of pairs of parallel lines is **2**.
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