Start with the meaning
NCERT connection: Grade 7 Ganita Prakash Part I, “Parallel and Intersecting Lines”. These are independent BananaLearn notes and original practice, not official NCERT material or a complete set of textbook exercise solutions. Match the chapter name to the book used by your school. Understand an angle, a straight angle of 180° and basic angle addition. The diagram shows selected angles; it is not a protractor measurement task.
Extend a line beyond the sketch
A mathematical line extends indefinitely in both directions. Two distinct lines in a plane are parallel if they never meet, however far they are extended. Short segments can look separate while their full lines intersect.
Perpendicular lines intersect at a right angle. They are a special case of intersecting lines, not a special case of parallel lines. Use the right-angle mark or a stated condition rather than relying on the drawing.
Use the relationships at one intersection
Adjacent angles forming a straight angle add to 180°. When two full lines intersect, vertically opposite angles are equal. These facts do not require another pair of parallel lines.
If one angle at an intersection is 63°, its vertically opposite angle is 63° and each adjacent angle is 117°. Name the relationship as you calculate, instead of applying 180° to every pair in the picture.
Add the parallel condition for a transversal
A transversal crosses two lines at different points. When those two lines are parallel, corresponding angles are equal and alternate interior angles are equal. Interior angles on the same side of the transversal add to 180°.
Corresponding means matching positions at the two intersections. Alternate interior means between the two parallel lines and on opposite sides of the transversal. Identify the positions first; the fact that two angles are near each other is not a rule.
Write a short chain of reasons
In the labelled diagram, the marked 60° angle and x are corresponding angles, so x = 60° because the horizontal lines are parallel. Angle y is adjacent to x on a straight line, so y = 120°.
If the parallel condition were removed, the corresponding-angle equality would no longer be guaranteed. A good solution records both the calculation and the condition that makes the rule valid. This also helps a parent see whether an error is in arithmetic or geometry.
Worked examples, step by step
Example 1: Two intersecting lines have one angle of 48°
- The vertically opposite angle is also 48°.
- Each adjacent angle is 180° − 48° = 132°.
- Check all four angles: 48 + 132 + 48 + 132 = 360°.
Example 2: A corresponding angle is 72° on parallel lines
- The transversal creates a second angle in the same relative position.
- Because the two crossed lines are parallel, that corresponding angle is 72°.
- An adjacent angle on its straight line is 180° − 72° = 108°.
Example 3: Same-side interior angles: one is 115°
- The lines are stated to be parallel. The two angles lie inside and on the same side of the transversal.
- They add to 180°, so the unknown is 180° − 115° = 65°.
- They are supplementary, not equal. Check 115 + 65 = 180.
Common mistakes and useful repairs
Using corresponding-angle equality without parallel lines
Check for a stated parallel condition or matching arrow marks. Similar-looking positions alone do not establish equal angles.
Calling adjacent angles vertically opposite
Vertically opposite angles do not share a side. Adjacent angles do. Trace the two rays of each angle before naming the relationship.
Try before revealing
Quick understanding check
Read the check answers
sum to 180°. They are supplementary under the parallel condition.
Vertically opposite angles are equal. Vertically opposite equality follows from intersecting lines.
Grade 7 parallel and intersecting lines: angle practice — practice sheet
Work on paper before opening an answer. Print this question sheet with or without a separate worked key; no account is needed.
Name: ____________________ Date: __________
One angle at an intersection is 37°. Find its vertically opposite angle.
Show answer and reasoning
37°. Vertically opposite angles are equal.
Find an angle adjacent to 37° on a straight line.
Show answer and reasoning
143°. 180 − 37 = 143.
Parallel lines are crossed by a transversal. One corresponding angle is 82°. Find the matching angle.
Show answer and reasoning
82°. Corresponding angles are equal when the lines are parallel.
Two same-side interior angles on parallel lines include 104°. Find the other.
Show answer and reasoning
76°. They sum to 180°, so 180 − 104 = 76.
One alternate interior angle on parallel lines is 59°. Find its partner.
Show answer and reasoning
59°. Alternate interior angles are equal under the parallel condition.
Perpendicular lines intersect. What is each of the four angles?
Show answer and reasoning
90°. Perpendicular lines form right angles.
In the illustrated diagram, find x and y.
Show answer and reasoning
x = 60°, y = 120°. x corresponds to 60°; y is adjacent to x on a straight line.
Two lines look parallel in a sketch but have no marks or stated condition. Can you assume corresponding angles are equal?
Show answer and reasoning
No. A rough drawing does not establish the needed parallel condition.
Grade 7 parallel and intersecting lines: angle practice — worked answer key
37°. Vertically opposite angles are equal.
143°. 180 − 37 = 143.
82°. Corresponding angles are equal when the lines are parallel.
76°. They sum to 180°, so 180 − 104 = 76.
59°. Alternate interior angles are equal under the parallel condition.
90°. Perpendicular lines form right angles.
x = 60°, y = 120°. x corresponds to 60°; y is adjacent to x on a straight line.
No. A rough drawing does not establish the needed parallel condition.
Choose the next practice step
Use the questions in this guide to practise this specific skill. If you need another explanation, return to Angles on a straight line: find missing angles with worked examples before trying a fresh problem.
Help at home: Ask which condition was used
Give your child one angle problem with parallel marks and one without them. Ask them to circle the given information and name a rule before calculating.
If they can calculate but cannot explain the rule, revisit one labelled intersection at a time. Rotating the paper should not change which angles are corresponding or vertically opposite.
Keep one example of your child’s own working. If the same confusion returns across fresh questions, share that attempt with their teacher and ask which next step fits their current learning.
Questions students and parents ask
Are these NCERT exercise solutions?
No. These are original questions with worked answers that support the named topic. Use the official textbook link for the book itself. Exercise numbers and school sequences can differ between editions.
How should a parent use the practice?
Ask for one independent attempt before revealing an answer. Notice whether the difficulty is reading the question, representing the idea or calculating. Revisit the matching example, then try a fresh question rather than copying the worked answer.
About this resource
BananaLearn created these explanations, diagrams and practice questions. They are not reproduced textbook or past-exam questions. School sequences differ; use the prerequisites to choose a starting point. Read how we prepare learning guides.
Curriculum and teaching references used to check scope:
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