CMDLearn

Learn

Class 7 Maths: A Tale of Three Intersecting Lines, 8 practice questions with answers

CMDLearn ·

These are 8 practice questions on A Tale of Three Intersecting Lines (Chapter 7) 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 triangle inequality, the possible lengths of a third side, where two circles meet, using mobile towers, which pairs of angles can belong to a triangle, an outside angle of a roof frame, an angle puzzle, two roads that never cross, and the types of triangles. 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 distinctive numbers is taken from the chapter, but 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 7, printed pages 146 to 172):

Sides

Question 1. Which of these sets of lengths (in cm) can be the sides of a triangle? (a) 6, 9, 16; (b) 7, 11, 17; (c) 4.5, 4.5, 9.

Answer: only (b). It is enough to check one thing: is the longest length shorter than the two other lengths added together? (a) 6 + 9 = 15, which is less than 16, so no triangle. (b) 7 + 11 = 18, which is more than 17, so the triangle inequality holds and a triangle exists. (c) 4.5 + 4.5 = 9, exactly equal to the longest length. The two shorter sides would lie flat along the longest one, so no triangle. (The triangle inequality, pages 151 to 154 and 159.)

Question 2. Two sides of a triangle are 8 cm and 13 cm. (a) Between which two lengths must the third side lie? (b) How many whole-number lengths in cm are possible for it?

Answer: (a) more than 5 cm and less than 21 cm; (b) 15 whole numbers, from 6 to 20. (a) If the third side is the longest, it must be less than 8 + 13 = 21 cm. If 13 cm is the longest, then 13 must be less than 8 plus the third side, so the third side must be more than 13 − 8 = 5 cm. (b) The whole numbers strictly between 5 and 21 are 6, 7, …, 20, which is 15 lengths. At exactly 5 or 21 the triangle would be flat. (Possible lengths of a third side, pages 159 and 160.)

Question 3. Two mobile towers stand 11 km apart. Is there any place that can get a signal from both towers, and if so, how much of the ground is that, when their ranges are (a) 4 km and 6 km; (b) 4 km and 7 km; (c) 5 km and 7 km?

Answer: (a) no place at all; (b) exactly one point, on the straight line between the towers; (c) a whole patch of ground. Picture a circle round each tower with its range as the radius, and compare the two ranges added together with the 11 km between the towers. (a) 4 + 6 = 10, less than 11: the circles do not meet, so no place is in reach of both. (b) 4 + 7 = 11, exactly the distance between them: the circles just touch, at one point on the line joining the towers, 4 km from the first. (c) 5 + 7 = 12, more than 11: the circles cross at two points, one on each side of the line, and the ground between those points is in reach of both. Either crossing point, with the two towers, makes a triangle with sides 11, 5 and 7 km. (The three cases for two circles, pages 157 to 159.)

Angles

Question 4. Which pairs can be two angles of a triangle? For those that can, find the third angle. (a) 64° and 118°; (b) 97° and 41°; (c) 90° and 90°.

Answer: only (b), with a third angle of 42°. Two angles can belong to a triangle only if their sum is less than 180°. (a) 64 + 118 = 182, which is more than 180, so no. (b) 97 + 41 = 138, less than 180, so yes, and the third angle is 180 − 138 = 42°. (c) 90 + 90 = 180: the two sides from the base would be parallel and never meet, so no. (Two angles and the included side, pages 162 to 164.)

Question 5. A triangular roof frame has one sloping beam carried on past the corner where it meets the floor beam, so that it makes an outside angle of 128° with the floor beam. One of the two angles of the frame that are away from that corner is 47°. Find (a) the frame's angle at that corner, next to the 128° angle, and (b) the frame's third angle.

Answer: (a) 52°; (b) 81°. (a) The frame's angle at that corner and the 128° outside angle lie along one straight beam, so together they make 180°: the corner angle is 180° − 128° = 52°. (b) The three angles of the frame add up to 180°, so the third angle is 180° − 47° − 52° = 81°. Check: 47° + 81° = 128°, the outside angle, as the angle sum and the straight angle together show. (The angle sum property, pages 164 to 166; exterior angles, page 167.)

Question 6. One angle of a triangle is 39°. Of the other two, one is twice the other. Find them.

Answer: 47° and 94°. The other two angles add up to 180° − 39° = 141°. If the smaller is x, the larger is 2x, so x + 2x = 141, which gives 3x = 141 and x = 47°; the larger is 94°. Check: 39 + 47 + 94 = 180. (The angle sum property, pages 165 and 166.)

Question 7. Two straight roads leave the two ends of a straight canal bank, both on the same side of the canal. The first road makes an angle of 52° with the bank. What is the smallest angle the second road can make with the bank, measured on the inside, so that the two roads never cross on that side?

Answer: 128°. The roads stop meeting at the angle where they become parallel. Then the bank is a transversal of two parallel lines, and the two interior angles on the same side add up to 180°, so the second road must make 180° − 52° = 128° with the bank. At any smaller angle the two roads would eventually cross; at 128° or more they never do. (When two angles cannot make a triangle, pages 162 and 163.)

Types of triangles

Question 8. Two angles of each triangle are given. Find the third angle and say whether each triangle is acute-angled, right-angled or obtuse-angled: (a) 33° and 57°; (b) 25° and 48°; (c) 61° and 62°. (d) A triangle has sides 7 cm, 7 cm and 10 cm. Is it equilateral, isosceles or scalene?

Answer: (a) 90°, right-angled; (b) 107°, obtuse-angled; (c) 57°, acute-angled; (d) isosceles. Each third angle is 180° minus the sum of the other two. (a) 180 − 90 = 90°, so the triangle is right-angled. (b) 180 − 73 = 107°, more than 90°, so it is obtuse-angled. (c) 180 − 123 = 57°; all three angles are less than 90°, so it is acute-angled. Having one acute angle is not enough: every triangle has at least two. (d) Two sides are equal, so it is isosceles; 7 + 7 = 14 is more than 10, so the triangle exists. (Types of triangles, page 170.)

Practise more, and check your marks

Where CMDLearn fits

CMDLearn is building an AI tutor for Classes 1 to 10 that explains a step and checks the child's working, but leaves the writing to the child. It is still in development, and no child uses it yet. If you would like to hear when there is something to try, you can join the waitlist.

Sources

All opened and read on 1 November 2026. Page numbers are the printed page numbers of the textbook; printed page = PDF page + 145 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: Intersecting Lines (triangles), Class 7 worksheet. Printable, in English, Hindi and Marathi, with an answer key.