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Parallel and Intersecting Lines — Hard

15 questions 18 min PYQ-grade reasoning

  1. Q1. Assertion (A): When two lines intersect, the vertically opposite angles are always equal. Reason (R): Each of the two angles forms a linear pair with the same third angle, and linear pairs add up to 180°.

  2. Q2. Consider these statements about the eight angles formed when a transversal cuts two lines: I. At each intersection, vertically opposite angles are equal. II. The eight angles can take at most four distinct measures. III. The eight angles can take exactly five distinct measures. Which are correct?

  3. Q3. Asha takes a square sheet and makes 4 horizontal folds, each fold halving an existing strip. Counting the two original horizontal edges along with all the fold lines, how many parallel lines does she see?

  4. Q4. Assertion (A): On a pair of parallel lines cut by a transversal, alternate angles are equal. Reason (R): An alternate angle equals a corresponding angle by vertically opposite angles, and corresponding angles on parallel lines are equal.

  5. Q5. Consider these statements about co-interior angles on parallel lines cut by a transversal: I. A co-interior angle equals a corresponding angle of the other parallel line. II. A co-interior angle and the corresponding angle on its own line form a linear pair. III. Hence the two co-interior angles add up to 180°. Which are correct?

  6. Q6. In Fig. 5.31, two parallel lines are cut by a transversal. An angle of 100° lies on one line and an angle of 42° lies between the transversal and the other line, both on the same side of the figure. Using alternate and adjacent angles, the value of a is

  7. Q7. In Fig. 5.31 (b), two parallel lines are cut by a transversal that makes an angle of 62° with one of them. The angle a is co-interior with the 62° angle. The value of a is

  8. Q8. In Fig. 5.32, two parallel lines are crossed by a transversal. At the upper intersection a small square marks a right angle, and an angle of 65° is shown. The angle x at the lower intersection is the alternate angle of (90° − 65°). The value of x is

  9. Q9. In Fig. 5.34, AB || CD || EF and EA is perpendicular to AB. If ∠BEF = 55°, then x = ∠DCE and y = ∠FCE satisfy

  10. Q10. In Fig. 5.35, line MN is parallel to line OP, and a zig-zag bends at point O. The hint is to draw a line through O parallel to MN and OP, splitting ∠NOP into two parts of 56° and 52°. The measure of ∠NOP is

  11. Q11. In Fig. 5.29, AB || CD and AD || BC, forming a parallelogram. ∠BCD = 120° is given. Consider: I. ∠DAB and ∠BCD are co-interior angles on transversal AB-CD-extended. II. ∠DAB = 120° by alternate-angle equality. III. ∠DAB = 60° because co-interior angles add to 180°. Which are correct?

  12. Q12. In Fig. 5.33, two parallel lines are cut by a transversal. It is given that ∠ABC = 45° and ∠IKJ = 78° at the two intersection points. By corresponding-angle equality on parallel lines, ∠FED equals

  13. Q13. Assertion (A): Every pair of perpendicular lines is also a pair of intersecting lines. Reason (R): Every pair of intersecting lines is also a pair of perpendicular lines.

  14. Q14. Meera wants to draw a line parallel to a given line l through a point P not on l, using a set square. Consider: I. She slides the set square along a fixed ruler. II. She keeps one edge of the set square along l throughout. III. The method works because corresponding angles between the slid edge and l stay equal. Which are correct?

  15. Q15. In Fig. 5.31 (c), two parallel lines are cut by a transversal. The transversal bends at point Q. On one parallel an angle of 110° is shown, and at the bend an angle of 35° is shown on the opposite side. Using a parallel line through Q, the value of a on the second parallel is

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