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Class 7 Maths: Parallel and Intersecting Lines, 8 practice questions with answers

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These are 8 practice questions on Chapter 5, Parallel and Intersecting Lines, of the new NCERT Class 7 Maths textbook, Ganita Prakash, Part 1. Each has a worked answer and the textbook page it comes from. They cover the angles where three lines meet at a point, linear pairs and perpendicular lines, corresponding angles along a ladder, a line at right angles to three parallel lines, alternate angles written as expressions, interior angles in a ratio, three parallel lines and one transversal, and when equal angles at a crossing need not be vertically opposite. Try each one on paper before you open the answer.

These questions are our own, drafted with AI help. Every number was re-computed by a test script, and none of the questions retells a worked example, activity or exercise from the chapter. No practising teacher has reviewed them yet. If you find a mistake, please tell us.

What the chapter says you need

Facts from the NCERT textbook (Ganita Prakash, Grade 7, Part 1, Chapter 5, printed pages 106 to 126):

Angles where lines cross

Question 1. Three straight paths in a park all pass through one fountain, O, so that six angles are formed around O. Two angles that sit next to each other measure 50° and 70°. Find all six angles, and say which rule gives each.

Answer: 50°, 70°, 60°, 50°, 70° and 60°, going round O. Each path is a straight line, so the three angles on one side of any path fill a straight angle: 50° + 70° + the third angle = 180°, which makes the third angle 60°. Each of the other three angles is vertically opposite to one of these, across a single path crossing, so they are 50°, 70° and 60° again. Check: 2 × (50 + 70 + 60) = 360°, a full turn. (Angles that fill a straight angle and vertically opposite angles, pages 107 and 108.)

Question 2. (a) Two angles form a linear pair, and one is 4 times the other. Find both. (b) Two lines cross and one of the angles is 90°. Show that all four angles are 90°, and say what such lines are called.

Answer: (a) 36° and 144°; (b) the lines are perpendicular. (a) Call the smaller angle x. Then x + 4x = 180°, so 5x = 180° and x = 36°; the other angle is 4 × 36° = 144°. (b) The angle next to the 90° angle makes a linear pair with it, so it is 180° − 90° = 90°. The opposite angles are vertically opposite to these, so they are 90° too. All four are right angles, so the lines are perpendicular. (Linear pairs, page 107; perpendicular lines, pages 108 and 109.)

Question 3. The rungs of a straight ladder are all parallel to one another, and one side rail crosses every rung. Where the rail meets the bottom rung, the angle above the rung on the outer side is 68°. (a) What is the angle above the fifth rung, in the same position? (b) What is the other angle at that rung, on the same side of the rail? (c) How many different angle measures are there at all the rung crossings together?

Answer: (a) 68°; (b) 112°; (c) 2 (68° and 112°). (a) The rail is a transversal of the parallel rungs, and the two angles are in the same position at their crossings, so they are corresponding angles, which are equal for parallel lines: 68°. (b) The two angles side by side above the rung form a linear pair: 180° − 68° = 112°. (c) Every rung is parallel to the bottom one, so each crossing repeats the same angles: only 68° and 112° occur. (Corresponding angles of parallel lines, page 117; linear pairs, page 107.)

Testing for parallel lines

Question 4. Three straight lines p, q and r are parallel, with q in the middle. A fourth straight line s crosses all three, and s is perpendicular to q. (a) What angle does s make with p, and with r? Give the reason. (b) A fifth line t passes through the point where s crosses q, and makes a 35° angle with q; this 35° angle lies inside one of the right angles between s and q. What is the angle between s and t at that point, and what angle does t make with r, in the same position?

Answer: (a) 90° with p and 90° with r; (b) 55° between s and t, and 35° with r. (a) For the lines p and q, s is a transversal. Its angle with q is 90°, and the angle in the same position at p is the corresponding angle. Corresponding angles are equal when the lines are parallel, so that angle is also 90°: s is perpendicular to p. The same reasoning with q and r gives 90° at r. So a line at right angles to one of three parallel lines is at right angles to all of them. (b) The right angle between s and q is split by t into two parts that add up to 90°, so the angle between s and t is 90° − 35° = 55°. t is also a transversal of the parallel lines q and r, so the angle it makes with r in the same position is a corresponding angle: 35°. (Corresponding angles of parallel lines, page 117; perpendicular lines, page 109; an angle split into two parts, page 108.)

Question 5. A transversal crosses two parallel lines. A pair of alternate angles measure (2x + 10)° and (3x − 25)°. Find x and the size of each angle, and then the interior angle on the same side as one of them.

Answer: x = 35; both angles are 80°; the interior angle on the same side is 100°. Alternate angles formed by a transversal crossing parallel lines are equal, so 2x + 10 = 3x − 25. Taking 2x from both sides gives 10 = x − 25, so x = 35. Then 2 × 35 + 10 = 80° and 3 × 35 − 25 = 80°. The interior angle on the same side as either of them adds up to 180° with it: 180° − 80° = 100°. (Alternate angles, page 120; interior angles, page 122.)

Question 6. Two shelves on a wall are parallel. A slanting wooden support runs from the upper shelf down to the lower one. The two angles the support makes with the shelves, between the shelves and on the same side of the support, are in the ratio 2 : 3. Find both angles.

Answer: 72° and 108°. The support is a transversal of the parallel shelves, and these are the two interior angles on the same side, which add up to 180°. Split 180° in the ratio 2 : 3: there are 2 + 3 = 5 equal parts, each 180° ÷ 5 = 36°, so the angles are 2 × 36° = 72° and 3 × 36° = 108°. Check: 72 + 108 = 180. (Interior angles on the same side add up to 180°, page 122.)

Three parallel lines, and a claim to test

Question 7. Three lines p, q and r are all parallel, with q between p and r. A transversal t crosses all three. At p, the angle above p and to the right of t is 58°. (a) What is the angle above r and to the right of t? (b) What is the angle below q and to the right of t? (c) Is the angle above q to the left of t equal to 58°, or to 122°?

Answer: (a) 58°; (b) 122°; (c) 122°. (a) p and r are parallel, so the angles at their crossings in the same position are corresponding angles and equal: 58°. (b) At q, the angle above and to the right of t is also 58° (corresponding to the one at p). The angle below it on the same side forms a linear pair with it: 180° − 58° = 122°. (c) Above q and to the left of t is the other angle of a linear pair with the 58° one above and to the right, so it is 122°. (Corresponding angles of parallel lines, page 117; linear pairs, page 107.)

Question 8. Priya says: "If two of the four angles where two lines cross are equal, they must be vertically opposite angles." (a) Find a case where she is wrong. (b) In that case, what can you say about all four angles?

Answer: (a) when the two equal angles sit next to each other; (b) then all four angles are 90° and the lines are perpendicular. (a) Two angles next to each other at a crossing form a linear pair and add up to 180°. If they are equal, each is 180° ÷ 2 = 90°. So two neighbouring angles can be equal without being vertically opposite, and Priya is wrong. (b) Their vertically opposite angles are then 90° as well, so all four angles are right angles and the lines are perpendicular. In every other crossing, two angles are equal only when they are vertically opposite. (Linear pairs and vertically opposite angles, pages 107 and 108; perpendicular lines, pages 108 and 109.)

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Sources

All opened and read on 1 November 2026. Page numbers are the printed page numbers of the textbook; printed page = PDF page + 105 for this chapter.

The rules are from the textbook pages above. The questions, worked answers and checks are our own, and every number was re-computed by script. This guide is general information; follow your teacher and the textbook.

Practise with the worksheet: Parallel & Intersecting Lines, Class 7 worksheet. Printable, in English, Hindi and Marathi, with an answer key.