CBSE Important Questions Class 7 Maths Chapter 5 Parallel and Intersecting Lines

CBSE Important Questions Class 7 Maths Chapter 5 – Parallel and Intersecting Lines

Class 7 Maths Chapter 5 Parallel and Intersecting Lines is a chapter of the new NCERT (National Council of Educational Research and Training) textbook Ganita Prakash. It explains what happens when two lines meet at a point (intersecting lines), when they never meet (parallel lines), and what angles are formed when a third line, called a transversal, crosses them. Students learn about acute, right and obtuse angles, angles on a straight line, and co-interior and corresponding angles.

These CBSE important questions for Class 7 Maths Chapter 5 are figure-based multiple choice questions on identifying an acute angle, finding an unknown angle on a straight line, recognising parallel lines, and using the angle rules for parallel lines cut by a transversal. Every question has a clear step-by-step answer in simple English, so students can practise on their own, parents can check the working, and teachers can use them in class. A free printable PDF of these important questions is also available on this page.

CBSE Important Questions Class 7 Maths Chapter 5 Parallel and Intersecting Lines

Parallel and Intersecting Lines (New NCERT)
Medium
Q.
​Can two straight lines intersect at more than one point?​
Parallel and Intersecting Lines (New NCERT)
Medium
Q.
​Can you draw a line parallel to l, that goes through point A? How will you do it with the tools from your geometry box? Describe your method.
Parallel and Intersecting Lines (New NCERT)
Medium
Q.
What is the measure of angle ∠NOP in Fig. 5.35?
Parallel and Intersecting Lines (New NCERT)
Medium
Q.
In Fig. 5.34, AB is parallel to CD and CD is parallel to EF. Also, EA is perpendicular to AB. If ∠BEF = 55°, find the values of x and y.
Parallel and Intersecting Lines (New NCERT)
Medium
Q.
​In Fig. 5.33, ∠ABC = 45° and ∠IKJ = 78°. Find angles ∠GEH, ∠HEF, ∠FED
Parallel and Intersecting Lines (New NCERT)
Medium
Q.
​In the figures below, what angles do x and y stand for?
Parallel and Intersecting Lines (New NCERT)
Medium
Q.
​Find the angle represented by a.
Parallel and Intersecting Lines (New NCERT)
Medium
Q.
Find the angles marked below.
Parallel and Intersecting Lines (New NCERT)
Medium
Q.
​In Fig. 5.13, which line is parallel to line a—line b or line c? How do you decide this?
​​
Parallel and Intersecting Lines (New NCERT)
Medium
Q.
Draw two lines on a plain sheet of paper so that they intersect. Measure the four angles formed with a protractor. Draw four such pairs of intersecting lines and measure the angles formed at the points of intersection.
​What patterns do you observe among these angles?​
Parallel and Intersecting Lines (New NCERT)
Medium
Q.
Using your sense of how parallel lines look, try to draw lines parallel to the line segments on this dot paper.
(a) Did you find it challenging to draw some of them?
(b) Which ones?
(c) How did you do it?
Parallel and Intersecting Lines (New NCERT)
Medium
Q.
In Fig. 5.11, mark the parallel lines using the notation given above (single arrow, double arrow etc.). Mark the angle between perpendicular lines with a square symbol.
(a) How did you spot the perpendicular lines?
(b) How did you spot the parallel lines?
Parallel and Intersecting Lines (New NCERT)
Medium
Q.
​Which pairs of lines appear to be parallel in Fig. 5.6 below?
​​
Parallel and Intersecting Lines (New NCERT)
Medium
Q.
​Observe Figure and describe the way the line segments meet or cross each other in each case, with appropriate mathematical words (a point, an endpoint, the midpoint, meet, intersect) and the degree measure of each angle. For example, line segments FG and FH meet at the endpoint F at an angle of 115.3°.
​Are line segments ST and UV likely to meet if they are extended?
Are line segments OP and QR likely to meet if they are extended?​​
Parallel and Intersecting Lines (New NCERT)
Medium
Q.
​List all the linear pairs and vertically opposite angles you observe in Fig.
Parallel and Intersecting Lines (New NCERT)
Medium
Q.

Claim: ∠a=∠c\angle a=\angle c  and ∠b=∠d\angle b=\angle d.
​​Is this always true for any pair of intersecting lines?​
Parallel and Intersecting Lines (New NCERT)
Medium
Q.
There do not seem to be any parallel lines here. Or, are there?

CBSE Important Questions Class 7 Maths Chapter 5 Parallel and Intersecting Lines

Q1. Refer to the given figure. Different angles are shown with angular arcs. Which one of them is an acute angle?
(a) ∠POQ
(b) ∠ROQ
(c) ∠POS
(d) ∠ROS

Rays OP, OQ, OR, OS and OT from point O

Answer: (a) ∠POQ
An acute angle is less than 90°. ∠POQ, between ray OP and ray OQ, is smaller than a right angle, so it is acute. ∠ROQ and ∠ROS are right angles (90°), and ∠POS is bigger than a right angle. So the acute angle is ∠POQ.

Q2. In the given figure, if XOY is a straight line, then the value of ∠XOA is
(a) 45°
(b) 65°
(c) 75°
(d) 115°

Straight line XOY with angle XOA = (x + 20) degrees and angle AOY = (2x + 25) degrees

Answer: (b) 65°
Angles on a straight line add up to 180°. So (x + 20) + (2x + 25) = 180
3x + 45 = 180, so 3x = 135 and x = 45
∠XOA = x + 20 = 45 + 20 = 65°
Check: ∠AOY = 2(45) + 25 = 115°, and 65° + 115° = 180° ✓

Q3. In the given figure, lines m and n, which do not intersect on extending infinitely, are
(a) parallel lines
(b) intersecting lines
(c) null
(d) transversal

Line l crossing lines m and n

Answer: (a) parallel lines
Lines that never meet, however far they are extended, are called parallel lines. Lines m and n keep the same distance apart everywhere, so they are parallel. Line l, which crosses both of them, is the transversal.

Q4. In the given figure, if i is parallel to m, then x is
(a) 100°
(b) 110°
(c) 120°
(d) 130°

Parallel lines i and m cut by transversal t, with angles 70 degrees and x

Answer: (b) 110°
The angles 70° and x lie between the two parallel lines on the same side of the transversal t. Such co-interior angles add up to 180°. So 70° + x = 180°, which gives x = 110°.

Related Study Material on Extramarks

Q.1 In the given figure, find the values of x, y, and z.

Marks:3
Ans

The given figure is:

From figure,
z = 90° (vertically opposite angles)
Now,
x, z, 30° lie on a straight line
By Linear Pair Axiom,
x + z + 30—¦ = 180°
x + 90° + 30° = 180°
x + 120° = 180—¦
x = 60°
And,
y = 30° (vertically opposite angles)
Hence, x = 60°, y = 30°, z=90°

Q.2 In the figure given below, PQ, RS, and UT are parallel lines.

If  measure of ∠c=57  and ∠a =∠c3, find the values of ∠a, ∠b and ∠d.

Marks:2
Ans

Given that : ∠c=57 and  ∠a = ∠c3∴∠a = 573= 19Since PQ UT,∠a + ∠b = ∠c alternate interior angles⇒19+ ∠b = 57⇒∠b = 57−19=38Also, PQ RS Given∠a + ∠d = 180 co−interior angles19+ ∠d = 180∠d = 180– 19= 161

Q.3 (i) Find the angle, which is equal to its complement.
(ii) Find the angle, which is equal to its supplement.

Marks:2
Ans

(i) Let x be the required angle.
Then x+x = 90° ⇒ 2x= 90° ⇒ x= 45°
Therefore, the angle which is equal to its complement is 45°.

(ii) Let x be the required angle.
Then x+x = 180° ⇒ 2x= 90° ⇒ x= 90°
Therefore, the angle which is equal to its supplement is 90°.

Q.4 In the given figure, lines l and m are parallel. What is the value of x?

Marks:1
1. 30°

2. 60°

3. 90°

4. 120°

Ans

3. 90°

Explanation

In the given figure draw a line, which is parallel to l and m as shown below.

∠1=60° (Alternate  angles)∠2=30° (Alternate  angles)∴x=∠1+∠2=60°+30°=90°

Q.5 What is the value of x, if l || m?

Marks:1
1.36°

2. 30°

3. 45°

4. 90°

Ans

1. 36°

Explanation

Since, l–m∴  2x+3x=180° (co-interior angles)⇒5x=180°⇒x=180°5=36°Hence, the required value of  x  is  36°.

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