Class 7 Maths · Original EZT practice
Parallel and Intersecting Lines (Class 7 Chapter 5): summary and practice
Railway tracks never meet; a crossing road cuts them. Chapter 5 studies lines that stay apart, lines that cross, and the angles a cutting line makes. All questions are original EZT tutor practice following the chapter's own section order. Edition note: this page covers the new NCERT book Ganita Prakash (Grade 7). Older Class 7 books numbered chapters differently - check your chapter title, not just the number.
8 original worked examples, 8 fresh self-check questions and 4 mixed questions, with explained answers. These are not copied textbook exercises, an official chapter index or a full answer key. No affiliation with NCERT is claimed.
Official sources for topic and edition context, checked 20 October 2026:
1. Intersecting, perpendicular and vertically opposite angles
Two lines that cross make four angles. Angles opposite each other at the crossing (vertically opposite) are equal. Angles side by side on a straight line add to one hundred eighty degrees. Lines meeting at ninety degrees are perpendicular.
2. Parallel lines and transversals
Parallel lines never meet and stay the same distance apart. A line that cuts two or more lines is a transversal. A transversal across two lines makes eight angles.
3. Corresponding angles
Angles in the same position at the two crossings are corresponding angles. When the two lines are parallel, corresponding angles are equal - and if they are equal, the lines are parallel.
4. Alternate angles and drawing parallels
Angles on opposite sides of the transversal, between the two lines, are alternate interior angles; for parallel lines they are equal. To draw a parallel line, copy an angle with a set square or ruler so that corresponding (or alternate) angles match.
Choose, solve, check, then try a fresh question.
Before calculating, read the method prompt and name the condition that makes it useful. Write your own attempt. Open the steps only when you need them, and use the check to catch a wrong sign, unit or interpretation. Finish with the fresh question before reading its answer.
Find all four angles where two lines cross
Choose the method: Use vertically opposite angles for the match, then the straight-line sum for the neighbours.
EZT practice question
Two lines cross; one angle is sixty-five degrees. Find the other three.
Show the worked solution
- The angle opposite is also sixty-five (vertically opposite angles are equal).
- Each neighbour forms a straight line with it: one hundred eighty minus sixty-five is one hundred fifteen.
- Both neighbours are one hundred fifteen.
Answer: Sixty-five, one hundred fifteen and one hundred fifteen degrees.
Check: Opposite angles match and each adjacent pair adds to one hundred eighty.
Watch for this: Do not make all four equal; only vertically opposite pairs are equal.
Now try it yourself
One angle of a crossing is one hundred ten degrees; give the other three.
Check your answer
One hundred ten, seventy and seventy degrees.
The opposite is equal and the neighbours complete the straight line.
Solve angles in a ratio on a straight line
Choose the method: Write the two parts as multiples of one unknown and use the straight-line sum.
EZT practice question
Angles x and three-x lie side by side on a straight line. Find x.
Show the worked solution
- Together they make a straight line: x plus three-x is one hundred eighty.
- Four-x is one hundred eighty, so x is forty-five.
- Then three-x is one hundred thirty-five.
Answer: x is forty-five degrees; the other angle is one hundred thirty-five degrees.
Check: Forty-five plus one hundred thirty-five is one hundred eighty.
Watch for this: Do not divide one hundred eighty by two; the parts are unequal, so use the total of the ratio parts.
Now try it yourself
Two angles on a straight line are two-y and seven-y; find y.
Check your answer
y is twenty.
Nine-y is one hundred eighty, so y is twenty.
Count the angles a transversal makes
Choose the method: Count the angles at each crossing separately, then add.
EZT practice question
How many angles does a transversal make with two lines?
Show the worked solution
- At each crossing of two lines, four angles form.
- The transversal crosses two lines, so there are two crossings.
- Four plus four is eight.
Answer: Eight - four at each crossing.
Check: Two crossings times four angles each gives eight.
Watch for this: Do not count only the angles between the two lines; every angle at both crossings counts.
Now try it yourself
Define a transversal.
Check your answer
A line that cuts two or more lines.
That is the chapter's definition.
Test whether lines can be parallel
Choose the method: Apply the definition: parallel lines never meet.
EZT practice question
Can two lines that meet at a point be parallel?
Show the worked solution
- Parallel lines never meet, however far they are extended.
- These two lines do meet.
- So they cannot be parallel.
Answer: No - parallel lines never meet.
Check: Meeting at even one point rules out being parallel.
Watch for this: Do not call lines parallel just because they look far apart near the crossing.
Now try it yourself
How many angles are formed where a transversal cuts two lines?
Check your answer
Eight.
Four angles form at each of the two crossings.
Use corresponding angles on parallel lines
Choose the method: Find the angle in the same position at the other crossing.
EZT practice question
A transversal cuts parallel lines; one angle at the top crossing is seventy degrees. What is the corresponding angle at the bottom?
Show the worked solution
- Corresponding angles sit in the same position at the two crossings.
- For parallel lines they are equal.
Answer: Seventy degrees.
Check: Equal corresponding angles are exactly what parallel lines guarantee.
Watch for this: Do not subtract from one hundred eighty; that is for neighbours on a line, not corresponding partners.
Now try it yourself
The bottom corresponding angle is forty-eight degrees; what is its partner above if the lines are parallel?
Check your answer
Forty-eight degrees.
Corresponding angles are equal on parallel lines.
Test parallel lines with corresponding angles
Choose the method: Compare the pair: equal means parallel, unequal means not.
EZT practice question
Corresponding angles are sixty-two and sixty-four degrees. Are the lines parallel?
Show the worked solution
- If the lines were parallel, corresponding angles would be equal.
- Sixty-two and sixty-four are not equal.
Answer: No - the corresponding angles are unequal, so the lines are not parallel.
Check: The test works both ways: equal angles prove parallel, unequal disprove it.
Watch for this: Do not call nearly equal angles equal; the test needs exact equality.
Now try it yourself
Corresponding angles are eighty-five and eighty-five degrees - are the lines parallel?
Check your answer
Yes.
Equal corresponding angles mean the lines are parallel.
Use alternate interior angles
Choose the method: The partner across the transversal is equal; its neighbour completes the straight line.
EZT practice question
Parallel lines are cut by a transversal; one alternate interior angle is fifty-five degrees. Find the other alternate angle and its neighbour on the same line.
Show the worked solution
- Alternate interior angles are equal on parallel lines: the other is fifty-five.
- Its neighbour on the straight line: one hundred eighty minus fifty-five is one hundred twenty-five.
Answer: The other alternate angle is fifty-five degrees; its neighbour is one hundred twenty-five degrees.
Check: Equal alternates plus a straight-line neighbour cover both facts.
Watch for this: Do not mix the two rules; equality is for the alternate partner, the sum is for neighbours.
Now try it yourself
An alternate angle is one hundred degrees; find its partner for parallel lines.
Check your answer
One hundred degrees.
Alternate interior angles are equal when the lines are parallel.
Test parallel lines with alternate angles
Choose the method: Compare the alternate pair for exact equality.
EZT practice question
Lines are cut by a transversal and the alternate angles are forty and forty-five degrees. Are the lines parallel?
Show the worked solution
- On parallel lines, alternate angles would be equal.
- Forty and forty-five differ.
Answer: No - the alternate angles are unequal.
Check: Unequal alternate angles can only happen when the lines are not parallel.
Watch for this: Do not ignore a small difference; any inequality breaks parallelism.
Now try it yourself
What is the neighbour of a one hundred degree angle on a straight line?
Check your answer
Eighty degrees.
Angles on a straight line add to one hundred eighty.
Try a mixed set
Choose a method or explanation before opening each answer.
1. What are vertically opposite angles?
Show answer and reason
Angles opposite each other where two lines cross; they are equal.
The crossing makes two such equal pairs.
2. What is a transversal?
Show answer and reason
A line that cuts two or more lines.
It makes eight angles with two lines.
3. What do we know about corresponding angles on parallel lines?
Show answer and reason
They are equal - and equal corresponding angles show the lines are parallel.
The fact works in both directions.
4. What are alternate angles?
Show answer and reason
Angles on opposite sides of a transversal between the two lines; equal for parallel lines.
They give another test for parallel lines.
Try it yourself
Work these on paper before checking any notes. Answers are deliberately not shown here.
- One angle where two lines cross is forty degrees - find the other three.
- Corresponding angles are seventy-one and seventy-one degrees - are the lines parallel? Give a reason.
- An alternate interior angle is sixty-five degrees - find its partner and its neighbour on the same line.
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Questions about this practice page
- What are vertically opposite angles?
- Angles opposite each other where two lines cross; they are always equal.
- What is a transversal?
- A line that cuts two or more lines.
- What do we know about corresponding angles on parallel lines?
- They are equal, and equal corresponding angles show the lines are parallel.
- What are alternate angles?
- Angles on opposite sides of a transversal between the two lines; they are equal for parallel lines.
- Are these the NCERT exercise questions for Parallel and Intersecting Lines?
- No. EZT pages are original practice following the chapter's section order - use them to prepare for the textbook exercises, not as a substitute for your book.