# NCERT Solutions for Class 7 Maths Chapter 5 Exercise 5.1

NCERT Solutions for Class 7 Maths Chapter 5 Exercise 5.1 (Ex. 5.1) Lines and Angles updated for new academic year 2020-2021 free to use online or download. All the solution are in PDF file format as well as videos format to learn in better way.

Class 7 math exercise 5.1 contains questions based on complementary angles, supplementary angles, linear pair, opposite angles and similar other concepts of lines and angles.## Class 7 Maths Chapter 5 Exercise 5.1 Solution

Class: 7 | Mathematics |

Chapter: 5 | Lines and Angles |

Exercise: 5.1 | Hindi and English Medium Solution |

### CBSE NCERT Class 7 Maths Chapter 5 Exercise 5.1 Solution in Hindi and English Medium

### Class 7 Maths Chapter 5 Exercise 5.1 Solution in Videos

#### Pairs of Angles

In geometry, we often come across pairs of angles. They have been given specific names.

##### Adjacent Angles

If two angles have:

(i) a common arm,

(ii) a common vertex and

(iii) their other arms lie on the opposite sides of the common arm, then the angles are called adjacent angles.

#### Linear Pair of Angles

A linear pair is a pair of adjacent angles formed when two lines intersect. If a ray stands on a line, then the two adjacent angles formed these are called linear pair of angles.

##### Supplementary Angles

Two angles are said to be supplementary if the sum of their measures is 180°.

Thus, angle A and angle B are supplementary if angle A + angle B = 180°.

Example:

If angle A = 75° and angle B = 105° then angle A and angle B are supplementary, since angle A + angle B = 180°.

##### Complementary Angles

Two angles are said to be complementary if the sum of their measures is 90°.

Thus, angle A and angle B are complementary if angle A + angle B = 90°.

Example:

If angle A = 36° and angle B = 54° then angle A and angle B are complementary angles, since angle A + angle B = 90°.

##### Find the complement of each of the following angles: (i) 60° (ii) 25°

(i) The given angle is 60°.

Let the measure of its complement be x°.

Then, x + 60 = 90

Or, x = (90 – 60) = 30°.

Hence, the complement of the given angle measures 30°.

(ii) The given angle is 25°.

Let the measure of its complement be x°.

Then, x + 25 = 90

Or, x = (90 – 25) = 65°.

Hence, the complement of given angle measures 65°.

##### Find the angles which is its own complement.

Let the measure of the required angle be x°.

Then, x + x = 90

Or, 2x = 90 Þ x = 45.

Hence, the required angle measures 45°.

##### Vertically Opposite Angles

Two angles are called a pair of vertically opposite angles if their arms form two pairs of opposite rays. Let two lines AB and CD intersect at a point O.

Then, two pairs of vertically opposite angles are formed:

(i) angle AOC and angle BOD

(ii) angle AOD and angle BOC.

##### How many pairs of angles are there?

Two interesting varieties of angle pairs sum to 180°. These are linear pairs and supplementary angles. Linear pairs get their name because the sides not common to the two angles form a straight line. Linear pairs always share a common vertex and one common ray, line segment, or line.

##### Can two angles be supplementary if both of them are acute or obtuse?

Thus, the two acute angles cannot be supplementary angles. Thus, the two obtuses angles cannot be supplementary angles. Thus, two right angles are supplementary angles.

##### What is a requirement of complementary angles?

The measures of complementary angles must add up to 90°. The measures of complementary angles must add up to 180°.