# Lines And Angles Chapter 5 Class 7 Maths NCERT Textbook With Solutions PDF

### Chapter 5: Lines and Angles

#### Checking For Parallel lines

If two lines are parallel, then you know that a transversal gives rise to pairs of equal corresponding angles, equal alternate interior angles, and interior angles on the same side of the transversal is supplementary.

When two lines are given, is there any method to check if they are parallel or not? You need this skill in many life-oriented situations.

A draftsman uses a carpenter’s square and a straight edge (ruler) to draw these segments (Fig 5.30). He claims they are parallel. How?

Are you able to see that he has kept the corresponding angles to be equal? (What is the transversal here?) Thus, when a transversal cuts two lines, such that pairs of corresponding angles are equal, then the lines have to be parallel. Look at the letter Z(Fig 5.31).

The horizontal segments here are parallel because the alternate angles are equal. When a transversal cuts two lines, such that pairs of alternate interior angles are equal, the lines have to be parallel

### NCERT Solutions Class 7 Maths Chapter 5 Lines and Angles

Q. Fill in the blanks:
(i) If two angles are complementary, then the sum of their measures is _.
(ii) If two angles are supplementary, then the sum of their measures is_____________.
(iii) Two angles forming a linear pair are ___.
(iv) If two adjacent angles are supplementary, they form a ___.
(v) If two lines intersect a point, then the vertically opposite angles are always.
(vi) (vi) If two lines intersect at a point and if one pair of vertically opposite angles are
acute angles, then the other pair of vertically opposite angles are_____________

#### Solution:

(i) 90°
(ii) 180°
(iii) Supplementary
(iv) Linear pair
(v) Equal
(vi) Obtuse angle

Exercise 5.1 (Page 101)

Q1. Find the complement of each of the following

Difficulty Level: Low

What is given/known
Measure of angles.

What is the unknown?
Measure of complementary angles.

Reasoning
The sum of complementary angles is always 90°. If the given angle is x, then we can find a complementary angle by subtracting ???? from 90°. Let us now find complement angles.

Solution:
(i) Given angle = 20°
Complement angle of 20° = 90° − ???????????????????? ????????????????????
= 90° − 20° = 70°

(ii) Given angle = 63°
Complement angle of 63° = 90° − ???????????????????? ????????????????????
= 90° − 63° = 27°
(iii) Given angle = 57°
Complement angle of 57° = 90° − ???????????????????? ????????????????????
= 90° − 57° = 33°

Q3. Identify which of the following pairs of angles are complementary and which
are supplementary:
(i) 65, 115 (ii) 63, 27 (iii) 112, 68 
(iv) 130, 50 (v) 45, 45 (vi) 80, 10

NOTE: The sum of the measure of a complementary angle is 90 and that of supplementary angle is 180.

Reasoning

Find out the sum of two given angles, and then check whether it is 180° ???????? 90°. If the sum of two angles is equal to 90°, the angles are complementary and if the sum of the two angles is 180°, the angles are complementary.

Solution:
Solve for supplementary angle or complementary angle:
(i) 65, 115
Sum of measure of these two angles = 65 + 115 = 180 Therefore, these two angles are supplementary.
(ii) 63, 27
Sum of measure of these two angles = 63 + 27 = 90 Therefore, these two angles are complementary.