Important Questions for CBSE Class 7 Maths Chapter 5 - Lines and Angles

Very Short Answer Type Questions 1- Mark

1. Define the following:

(a) Adjacent Angles

Ans: The angles are said to be adjacent only if they have a common arm/side and a common vertex and they do not overlap.

(b) Supplementary Angles

Ans: When the sum of two angles is ${180^\circ }$, then they are said to be supplementary angles.

(c) Complementary Angles

Ans: When the sum of two angles is ${90^\circ }$, then they are said to be complementary angles.

(d) Linear Pair of Angles

Ans: When a straight line is divided into two parts, i.e., two different angles. Then those angels are said to be linear pairs.

The measure of a straight angle is ${180^\circ }.$ So a linear pair of angles must add up to ${180^\circ }$.

(e) Vertically Opposite Angle

Ans: When two lines cross then they share the same vertex, vertically opposite angles are the angles opposite to one another having a common vertex.

Short Answer Type Questions 2- Marks

2. Write the complementary angle of ${57^\circ }$.

Ans: The sum of complementary angles is ${180^\circ }$.

Let the other angle be x, then

$x + {57^\circ } = {90^\circ }$

$x = {90^\circ } - {57^\circ }$

 $x = {33^\circ }$ 

3. Write the supplementary angle of ${103^\circ }$.

Ans: The sum of complementary angles is ${180^\circ }$.

Let the other angle be x, then

$x + {103^\circ } = {180^\circ }$

$x = {180^\circ } - {103^\circ }$

$x = {77^\circ }$ 

4. Find the value of x in the given figure.

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Ans:

$ACB{\text{ is a straight line}}{\text{.}}$

$\therefore \,\,\angle ACD + \angle BCD = {180^{\circ \,}}\,\,\,\,\left( {{\text{Linear}}\,{\text{pair}}} \right)$

$x + {130^\circ } = {180^\circ }$

$x = {180^\circ } - {130^\circ }$

$x = {50^\circ }$ 

5. Identify the supplementary and complementary angles.

1. ${60^\circ },\,\,{120^\circ }$

2. ${30^\circ },\,\,{60^\circ }$

3. ${35^\circ },\,\,{145^\circ }$

4. ${12^\circ },\,\,{78^\circ }$

Ans: Pair of angles whose sum is ${180^\circ }$ are called supplementary angles.

Here,

${60^\circ },\,\,{120^\circ }$ and ${35^\circ },\,\,{145^\circ }$ are supplementary angles.

Pair of angles whose sum is ${90^\circ }$ are called complementary angles.

Here,

${30^\circ },\,\,{60^\circ }$ and ${12^\circ },\,\,{78^\circ }$ are complementary angles.

6. In the following figures is $\angle 1{\text{ and }}\angle 2$ are adjacent? Give reason.

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Ans: Adjacent angles are those that arise from the same vertex and have one arm/side in common.

Here,

$\angle 1{\text{ and }}\angle 2$ has a common arm/side but since they do not have a common vertex. Therefore, the angles are not adjacent.

7. Find the value of \[x,\,y\,{\text{ and }}z\].

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Ans: From the figure it is clear that $\angle x$ and ${50^\circ }$ are vertically opposite angles

$\therefore \angle x = {50^\circ }$

$\angle x + \angle y = {180^\circ }\,\,\,\,\,\,\,\,\,\,\,\left( {{\text{Linear pair}}} \right)$

${50^\circ } + \angle y = {180^\circ }$

$\angle y = {180^\circ } - {50^\circ }$

$\angle y = {130^\circ }$ 

Similarly, $\angle y$ and $\angle z$ are vertically opposite angles.

$\therefore \angle y = \angle z = {130^\circ }$

8. If $\angle ABC = {55^\circ }$, then find

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1. $\mathbf{\angle DGC}$

Ans: From the figure we can conclude that  and a traversal line ${\text{BC}}$ is intersecting them.

$\angle DGC = \angle ABC\,\,\,\,\,\,\,\left( {{\text{corresponding angles}}} \right)$

$\therefore \angle DGC = {55^\circ }$

2. $\mathbf{\angle DEF}$

Ans: From the figure we can conclude that a traversal line DE is intersecting them.

$\angle DEF = \angle DGC\,\,\,\,\,\,\,\,\left( {{\text{corresponding angles}}} \right)$

$\therefore \angle DEF = {55^\circ }$ 

9. Find the angle which is equal to its complement.

Ans: Let the angle equal to its complement be ${\text{x}}$.

Since the complement of this angle is also ${\text{x}}$. Therefore,

The sum of the measures of a complementary angle pair is ${90^\circ }$.

$x + x = {90^\circ }\,\,\,\,\,\,\,\,\,\,\left( {{\text{complementary angles}}} \right)$

$\,\,\,\,\,2x = {90^\circ }$

$\,\,\,\,\,\,\,x = {45^\circ }$ 

10. Find the angle which is equal to its supplement.

Ans: Let the angle equal to its supplement be ${\text{x}}$.

Since the supplement of this angle is also ${\text{x}}$. Therefore,

The sum of the measures of a supplementary angle pair is ${180^\circ }$.

$x + x = {180^\circ }$

$\,\,\,\,\,2x = {180^\circ }$

$\,\,\,\,\,\,\,\,x = {90^\circ }$ 

Short Answer Type Questions   3 - Marks

11. Find the value of \[x,\,y\,{\text{ and }}z\] in each of the following:

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Ans:

$\angle z = {30^\circ }$ (vertically opposite angles)

$\angle y + \angle z = {180^\circ }$ (linear pair)

$\angle y + {30^\circ } = {180^\circ }$

$\,\,\,\,\,\,\,\,\,\,\,\,\angle y = {150^\circ }$ 

${30^\circ } + \angle x + {30^\circ } = {180^\circ }$ (angles on a straight line)

${60^\circ } + \angle x = {180^\circ }$

$\,\,\,\,\,\,\,\,\,\,\,\angle x = {120^\circ }$ 

12. In the adjoining figure, identify:

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(a) The Pairs of Corresponding Angles

Ans: When two parallel lines are intersected by any other line and the angle formed in the corresponding corner are called corresponding angles.

Here,

$\angle 1$ and $\angle 5,\,\,\,\angle 2$ and $\angle 6,\,\,\,\angle 3$ and $\angle 7,\,\,\,\angle 4$ and $\angle 8$

(b) The Pairs of Alternate Angles

Ans: they are the angles that lie on the inner side of the parallel lines but on the opposite sides of the transversal. 

$\angle 3$ and $\angle 5,\,\,\,\angle 4$ and $\angle 6$

(c) The Pairs of Interior Angles on the Same Side of Traversal

Ans: when a pair of the parallel lines is intersected by a transversal, the pair of interior angles on the same side of the transversal are supplementary (sum to 180°).

$\angle 4$ and $\angle 5,\,\,\,\angle 3$ and $\angle 6$

 (d) Vertically Opposite Angles

Ans: When two lines cross then they share the same vertex, vertically opposite angles are the angles opposite to one another having a common vertex.

$\angle 1$ and $\angle 3,\,\,\,\angle 2$ and $\angle 4,\,\,\,\angle 5$ and $\angle 7,\,\,\,\angle 6$ and $\angle 8$

13. Find the value of $x$ in the following figure.

Ans: From the figure, line $l$ is parallel to $m$ and a transversal passes through them. Hence,

$\angle y = {105^\circ }$ (corresponding angles)

$\angle x + \angle y = {180^\circ }$

$\angle y = {180^\circ } - {105^\circ }$

$\angle y = {75^\circ }$ 

14. Find the value of ${\text{x}}$ in each of the following figures is a parallelogram.

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Ans: From the figure, line $l$ is parallel to $m$ and a transversal passes through them. Hence,

$\angle x = {120^\circ }$ (corresponding angles)

15. In the given figure check whether parallelogram.

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Ans: Consider a pair of parallel lines l and m and a traversal line n which intersects them. Sum of the interior angles on the same side of traversal,

 $ = {116^\circ } + {54^\circ } = {170^\circ }$

As the sum of interior angles on the same side of traversal is not ${180^\circ }$.

Therefore, l is not parallel to m.

Lines and Angles Class 7 Important Questions

Nearly every aspect of our everyday lives includes lines and angles. To excel in the exams, students must be competent in calculating angles, measuring angles, and drawing angles. However, a proper understanding of lines and angles is essential for understanding the universal problems on lines and angles.

Let us have a look at important topics from the Lines and Angles Chapter.

• Basic Terms and Definitions

• Intersecting Lines and Non-intersecting Lines

• Pairs of Angles

• Parallel Lines and a Transversal

• Lines Parallel to the Same Line

• Angle Sum Property of a Triangle

Chapter 5 - Lines and Angles

Line

A line is a one-dimensional figure that is parallel, has no thickness, and stretches in both directions indefinitely. It's commonly referred to as the shortest distance between two points.

There are 2 Types of Lines:

• Intersecting Lines

Intersecting lines are created when two or more lines in a plane cross each other. The point of intersection is where the intersecting lines share a common point that occurs on all intersecting lines.

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• Non-Intersecting Lines

Non-intersecting lines are made up of two or more lines that do not intersect. These lines that do not intersect will never cross. The parallel lines are another name for them. They remain at the same distance from one another at all times.

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Angles

In geometry, an angle is known as the figure created by two rays meeting at a common endpoint.

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Pairs of Angles

• Complementary Angles

If the degree measurements of two angles add up to 90 degrees, they are complementary angles. That is, if we link both angles and position them next to each other, they will form a right angle.

• Supplementary Angles

If the sum of the degree measurements is 180° and one angle is said to be the supplement of the other then these angles are called supplementary angles. If we put the angles side by side, we get a straight line in supplementary angles.

• Vertical Angles

At the intersection of two sides, vertical angles are the angles that are opposite each other. Since they have a common vertex, they are called vertical angles.

• Alternate Interior Angles

When a transversal occurs, alternate interior angles are created. They are the angles on opposite sides of the transversal, but the transversal intersects inside the two lines. If the two lines intersected by the transversal are parallel, alternate interior angles are congruent.

• Alternate Exterior Angles

Alternate exterior angles are congruent to each other in the same way as alternate interior angles are if the two lines intersected by the transversal are parallel. These angles are on opposite sides of the transversal, but the transversal intersects outside of the two lines.

• Corresponding Angles

The pairs of angles on the same side of the transversal and on the corresponding sides of the two other lines are known as corresponding angles. When the two lines intersected by the transversal are parallel, these angles are equal in degree measure.

Benefit of Important Questions for CBSE Class 7 Chapter 5- Lines and Angles

The benefits of "Important Questions for CBSE Class 7 Maths Chapter 5 - Lines and Angles" are significant and multifaceted.

Firstly, these questions are strategically designed to reinforce and consolidate the fundamental concepts of lines and angles. They serve as a valuable tool for revision, helping students gauge their understanding of the chapter.

Secondly, these important questions enhance problem-solving skills. By tackling a variety of questions that span different difficulty levels, students develop critical thinking and analytical abilities, which are essential not only in mathematics but also in various aspects of life.

Furthermore, these questions prepare students comprehensively for examinations. They cover a wide spectrum of topics within the chapter, ensuring that students are well-equipped to excel in assessments. The questions encourage practical application of geometric principles, allowing students to see the real-world relevance of lines and angles. Overall, these important questions serve as an essential resource that not only aids in academic success but also fosters holistic mathematical development.

Conclusion

Lines and Angles is one of the most scoring topics for Class 7 students. Students can download the free PDF for Lines and Angles Class 7 Important Questions from Vedantu to prepare for their exams. We provide step-by-step solutions to help students understand the concepts easily. All solutions are according to the CBSE guidelines. So download the Class 7 Maths Chapter 5 Extra Questions and prepare well for your exams.