CBSE Class 7 Mathematics Parallel and Intersecting Lines Practice Paper Worksheet Set 03 with Answers

Class 7 Maths Ganita Prakash Chapter 5 Parallel and Intersecting Lines Practice Paper 15 (CBSE) has 20 questions worth 40 marks, arranged in Sections A to E, each followed by a clear worked solution. This paper focuses on reading figures: spotting parallel lines on a dot grid, using corresponding, alternate and co-interior angles, finding a reflex angle by drawing an extra parallel line through a bend, and chasing angles through a triangle and two pairs of parallel lines. The case studies use a transversal with numbered angles and the support beams of an overbridge.

Section A: Multiple Choice Questions (1 Mark Each)

Section B: Short Answer Questions (2 Marks Each)

Question 11. In the figure below, identify all the parallel lines.

Answer:
Lines that never meet, however far they are extended, and that run in the same direction on the grid are parallel.
Vertical lines: a ∥ i ∥ h.
Horizontal lines: c ∥ g.
Lines going down to the right, one dot across for one dot down: d ∥ f.
Lines going up to the right, one dot across for one dot up: b ∥ e.
In simple words: a, i, h are parallel; c and g are parallel; d and f are parallel; b and e are parallel.

Teacher's Note:
1. On a dot grid, compare how many dots a line moves across and down.
2. Lines in the same direction are parallel even if they are different lengths.

Question 12. Two lines intersect at a point O. ∠1 and ∠3 are vertically opposite angles. If ∠1 = 2x and the adjacent angle ∠2 = 3x, find the measure of ∠1.
Answer:
∠1 and ∠2 are adjacent angles on a straight line, so they form a linear pair: 2x + 3x = 180°.
5x = 180°, so x = 36°.
∠1 = 2 × 36° = 72° (and ∠3 = 72° too).
In simple words: 2x + 3x = 180 gives x = 36, so ∠1 = 72°.

Teacher's Note:
1. The original said 'three lines'; with three lines the adjacent angles need not add to 180°, so it was changed to two lines.
2. Check: ∠2 = 108° and 72° + 108° = 180°.

Question 13. A transversal cuts two parallel lines. If the sum of two vertically opposite angles at one intersection is 150°, find the measures of the two interior angles on the same side of the transversal.
Answer:
Vertically opposite angles are equal, so each is 150° ÷ 2 = 75°.
So the angles at that crossing are 75°, 105°, 75°, 105°, and the same angles appear at the other crossing.
The interior angles on the same side add up to 180°: one is 75°, the other is 180° − 75° = 105°.
The two interior angles are 75° and 105°.
In simple words: Each opposite angle is 75°, so the co-interior angles are 75° and 105°.

Teacher's Note:
1. 'Consecutive interior angles' in the original means interior angles on the same side.
2. Same-side interior angles are supplementary.

Question 14. Two complementary angles are such that one angle is 10° more than the other. Find the measure of the larger angle.
Answer:
Let the smaller angle be y°. The larger is (y + 10)°.
y + (y + 10) = 90, so 2y = 80 and y = 40.
Larger angle = 40° + 10° = 50°.
In simple words: The angles are 40° and 50°, so the larger is 50°.

Teacher's Note:
1. Complementary angles add up to 90°.
2. Check: 50° − 40° = 10°.

Section C: Short Answer Questions (3 Marks Each)

Question 15. In the adjoining figure, l ∥ m and t is a transversal. If ∠2 = 120°, find all the other angles.

Answer:
∠4 is vertically opposite to ∠2: ∠4 = 120°.
∠1 and ∠2 form a linear pair: ∠1 = 180° − 120° = 60°, and ∠3 (opposite ∠1) = 60°.
Since l ∥ m, corresponding angles are equal: ∠6 = ∠2 = 120°, ∠8 = ∠4 = 120°, ∠5 = ∠1 = 60°, ∠7 = ∠3 = 60°.
∠1 = ∠3 = ∠5 = ∠7 = 60° and ∠4 = ∠6 = ∠8 = 120°.
In simple words: The wide angles are all 120° and the narrow angles are all 60°.

Teacher's Note:
1. The arrow marks on l and m show that they are parallel; this was added to the question.
2. Every acute angle plus every obtuse angle here makes 180°.

Question 16. Find the values of x and y in the given figure, if l ∥ m and p ∥ q.

Answer:
At the top, l and p make an angle of 100°.
l ∥ m and p is a transversal, so x (between m and p, in the same position) is a corresponding angle: x = 100°.
At the left crossing, z is vertically opposite to the 80° angle, so z = 80°.
p ∥ q and m is a transversal. At the bottom crossing, the angle between m and q that opens upwards is in the same position as x, so it is also 100° (corresponding angles).
y is vertically opposite to that angle, so y = 100°. (Check: l ∥ m and q is a transversal, so y and z are co-interior partners: y = 180° − 80° = 100°.)
Answer: x = 100°, y = 100°.
In simple words: Corresponding angles copy the 100° angle to x and to y.

Teacher's Note:
1. The 80° angle is the co-interior partner of 100°, which confirms the figure.
2. z = 80° is an extra unknown you can find on the way.

Question 17. In the given figure, if l ∥ m, find the value of x.

Answer:
Through O draw a line n parallel to l (and so parallel to m), pointing to the left.
l ∥ n and OP is a transversal, so the angle between OP and n is 35° (alternate interior angles).
n ∥ m and OQ is a transversal, so the angle between OQ and n is 40° (alternate interior angles).
∠POQ = 35° + 40° = 75°.
x is the reflex angle POQ: x = 360° − 75° = 285°.
In simple words: The small angle at O is 35° + 40° = 75°, so the marked reflex angle is 285°.

Teacher's Note:
1. The original said 'l ∥ n', but the lines are named l and m; it was corrected.
2. Draw a helper parallel line through the bend.
3. Notice the arc for x goes the long way round O.

Section D: Long Answer Question (5 Marks)

Question 18. In the figure, AB ∥ CE and CD ∥ EF. Find the value of x.

Answer:
In triangle ABC, the angle sum is 180°: ∠1 + 40° + 65° = 180°, so ∠1 = 75°.
AB ∥ CE and AD is a transversal, so ∠2 = ∠1 = 75° (corresponding angles).
A, C, D lie on a straight line: 65° + ∠3 + ∠2 = 180°, so ∠3 = 180° − 65° − 75° = 40°.
(Also ∠3 = ∠ABC = 40° as alternate angles, since AB ∥ CE and BC is a transversal.)
So ∠ECA = 65° + 40° = 105°.
EF ∥ AD (because CD ∥ EF) and EC is a transversal, so ∠CEF = ∠ECA (alternate interior angles).
x = 105°.
In simple words: ∠1 = 75°, ∠2 = 75°, ∠3 = 40°, and x = 65° + 40° = 105°.

Teacher's Note:
1. Use the triangle angle sum first.
2. Then use AB ∥ CE to move the angle at A to C.
3. Check: x and ∠2 are co-interior angles, so x + 75° = 180°.

Section E: Case Study Based Questions (4 Marks Each)

Question 19. Case Study 1: Two lines are parallel to each other if the distance between them always remains the same and they never meet. Examples of parallel lines in daily life are railway lines, two steps of a ladder and the opposite sides of a table. A line which cuts a pair of parallel lines is called a transversal, as shown in the figure, where CD ∥ AB and LM is a transversal.
(a) If ∠5 = 65°, then what is ∠8? (1 mark)
(b) If ∠6 = 2x and ∠1 = 70°, then find the value of x. (1 mark)
(c) If ∠6 : ∠5 = 2 : 3, then find the value of ∠7. (2 marks)
Answer:
(a) ∠5 (above CD, right of LM) and ∠8 (below AB, left of LM) are alternate exterior angles, so ∠8 = ∠5 = 65°.
(b) ∠1 and ∠5 are corresponding angles, so ∠5 = 70°. ∠6 and ∠5 form a linear pair: 2x + 70 = 180, so 2x = 110 and x = 55.
(c) Let ∠6 = 2k and ∠5 = 3k. They form a linear pair: 5k = 180°, so k = 36° and ∠6 = 72°.
∠6 (above CD, left of LM) and ∠7 (below AB, right of LM) are alternate exterior angles, so ∠7 = ∠6 = 72°.
In simple words: (a) 65°, (b) x = 55, (c) ∠7 = 72°.

Teacher's Note:
1. Alternate exterior angles lie outside the parallel lines on opposite sides of the transversal.
2. Each part is a separate 'if'; do not mix the values.
3. The photos of the track, ladder and table are only examples.

Question 20. Case Study 2: Overbridge Support Beams An overbridge is supported by two parallel beams (lines l and m). A diagonal support rod t (a transversal) connects the beams and creates corresponding angles ∠a and ∠b. Workers measure ∠a = 68°. To check stability, they want to verify that the beams remain parallel by measuring these angles. The second figure (for part iv) shows a ray OC standing on line AB.
(i) What is the measure of ∠b?
(ii) Which property relates ∠a and ∠b?
(iii) What should be the sum of the interior angles on the same side of the transversal?
(iv) In the given figure, find the value of x.
Answer:
(i) ∠a and ∠b are corresponding angles and l ∥ m, so ∠b = ∠a = 68°.
(ii) The corresponding angles property: when a transversal cuts two parallel lines, corresponding angles are equal (and if they are equal, the lines are parallel).
(iii) Interior angles on the same side of the transversal are supplementary: their sum is 180°.
(iv) Ray OC stands on line AB, so ∠AOC + ∠BOC = 180°: 4x + 2x = 180°, so 6x = 180° and x = 30°.
In simple words: ∠b = 68° (corresponding angles), same-side interior angles add to 180°, and x = 30°.

Teacher's Note:
1. Corresponding angles sit in matching corners.
2. In (iv), 4x and 2x are a linear pair, so the angles are 120° and 60°.
3. The photo of the bridge is decorative.