CBSE Class 7 Lines And Angles Worksheet With Solutions

Lines and angles are fundamental concepts in geometry that are essential for understanding more complex shapes and figures. In this worksheet, students will explore the properties of lines and angles, learn how to classify them, and solve problems related to their relationships. By mastering these concepts, students will develop a strong foundation in geometry and problem-solving skills.

Lines and Angles Worksheet 1 With Solutions

1. Define the following terms:
   a. Line
   b. Ray
   c. Line segment
   d. Angle
2. Classify the following lines as parallel, intersecting, or perpendicular:
   a. Two lines that have no common point
   b. Two lines that have exactly one common point
   c. Two lines that form right angles
3. Identify the type of angle formed by the following pairs of lines:
   a. Two intersecting lines
   b. Two parallel lines cut by a transversal
   c. Two perpendicular lines
4. Find the measure of the angle formed by the hands of a clock at 3:00 PM.
5. If two angles are supplementary, what is the sum of their measures?
6. If two angles are complementary, what is the sum of their measures?
7. Find the measure of an angle that is 30° less than another angle.
8. If the measure of an angle is three times the measure of another angle, and their sum is 180°, find the measure of each angle.
9. Two angles are in the ratio 3:5. If their sum is 120°, find the measure of each angle.
10. Find the measure of an angle that is 45° more than another angle.

Solutions

1. Definitions
   a. Line: A line is a straight path that extends infinitely in both directions.
   b. Ray: A ray is a part of a line that has one endpoint and extends infinitely in one direction.
   c. Line segment: A line segment is a part of a line that has two endpoints and a definite length.
   d. Angle: An angle is the figure formed by two rays that share a common endpoint called the vertex.
2. Classifying lines:
   a. Parallel lines: Two lines that have no common point
   b. Intersecting lines: Two lines that have exactly one common point
   c. Perpendicular lines: Two lines that form right angles
3. Identifying angle types:
   a. Intersecting lines form adjacent angles and vertical angles.
   b. Parallel lines cut by a transversal form alternate interior angles, alternate exterior angles, corresponding angles, and interior angles on the same side of the transversal.
   c. Perpendicular lines form right angles.
4. Angle formed by clock hands at 3:00 PM: 90°
5. Sum of supplementary angles: 180°
6. Sum of complementary angles: 90°
7. Angle that is 30° less than another angle: (x – 30)°
8. Measure of each angle: 45°
9. Measure of each angle: 48° and 72°
10. Angle that is 45° more than another angle: (x + 45)°

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Lines and Angles Worksheet 2 With Solutions

Section 1: Multiple Choice Questions

1. What is the sum of the measures of two complementary angles?
   a) 90°
   b) 180°
   c) 360°
   d) 450°

Answer: a) 90°

2. What is the sum of the measures of two supplementary angles?
   a) 90°
   b) 180°
   c) 360°
   d) 450°

Answer: b) 180°

3. What is the measure of an angle that is supplementary to 75°?
   a) 75°
   b) 105°
   c) 120°
   d) 150°

Answer: b) 105°

Section 2: Short Answer Questions

1. Find the measure of an angle that is complementary to 45°.

Solution: The measure of the complementary angle is 45°.

2. Find the measure of an angle that is supplementary to 120°.

Solution: The measure of the supplementary angle is 60°.

3. Identify the pairs of adjacent angles in the figure below.

Solution: The pairs of adjacent angles are ∠AOE and ∠EOC, ∠EOC and ∠COB, ∠AOC and ∠COB, ∠COB and ∠BOD, and ∠EOB and ∠BOD.

Section 3: Long Answer Questions

1. In the figure below, ∠ROS is a right angle and ∠POR and ∠QOS are in the ratio 1 : 5. Find the measure of ∠QOS.

Solution: ∠POR and ∠QOS are in the ratio 1 : 5. Therefore, ∠QOS = 5 × ∠POR. Since ∠ROS is a right angle, ∠POR + ∠QOS = 90°. Therefore, ∠QOS = 5 × ∠POR = 5 × (90° – ∠POR) = 450° – 5 × ∠POR. This equation can be solved for ∠POR, and then ∠QOS can be found.

2. Find the measure of an angle that is supplementary to 27°.

Solution: The measure of the supplementary angle is 153°.

3. In the figure below, if QP || SR, find the value of a.

Solution: Since QP || SR, ∠QOS and ∠TSO are co-interior angles. Therefore, ∠QOS = ∠TSO. Also, ∠QOS + ∠TSO = 180°. Therefore, a = 85°.