# Lines and Angles 5.1

Samrules
Published at : 12 Dec 2020
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Full exercise on Lines and Angles, fully solved. This is a video tutorial for 7th class NCERT CBSE students.

RELATED ANGLES
Complementary Angles
When the sum of the measures of two angles is 90°, the angles are called complementary angles. Whenever two angles are complementary, each angle is said to be the complement
of the other angle.

THINK, DISCUSS AND WRITE
1. Can two acute angles be complement to each other?
2. Can two obtuse angles be complement to each other?
3. Can two right angles be complement to each other?

Supplementary Angles
When two angles are supplementary, each angle is said to be the supplement of the other.
THINK, DISCUSS AND WRITE
1. Can two obtuse angles be supplementary?
2. Can two acute angles be supplementary?
3. Can two right angles be supplementary?

What will be the measure of the supplement of each one of the following angles?
(i) 100º (ii) 90º (iii) 55º (iv) 125º
3. Among two supplementary angles the measure of the larger angle is 44º more than the measure of the smaller. Find their measures.

These angles are such that:
(i) they have a common vertex;
(ii) they have a common arm; and
(iii) the non-common arms are on either side of the common arm.
Such pairs of angles are called adjacent angles. Adjacent angles have a common vertex and a common arm but no common interior points.

THINK, DISCUSS AND WRITE
1. Can two adjacent angles be supplementary?
2. Can two adjacent angles be complementary?
3. Can two obtuse angles be adjacent angles?
4. Can an acute angle be adjacent to an obtuse angle?

Linear Pair A linear pair is a pair of adjacent angles whose non-common sides are opposite rays.

THINK, DISCUSS AND WRITE
1. Can two acute angles form a linear pair?
2. Can two obtuse angles form a linear pair?
3. Can two right angles form a linear pair?

Vertically Opposite Angles
We conclude that when two lines intersect, the vertically opposite angles so formed are equal.

EXERCISE 5.1
1. Find the complement of each of the following angles:

2. Find the supplement of each of the following angles:

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

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

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

6. In the given figure, ∠1 and ∠2 are supplementary
angles. If ∠1 is decreased, what changes should take place in ∠2 so that both the angles still remain supplementary.

7. Can two angles be supplementary if both of them are:
(i) acute? (ii) obtuse? (iii) right?

8. An angle is greater than 45º. Is its complementary angle greater than 45º or equal to 45º or less than 45º?

(i) Is ∠1 adjacent to ∠2?
(ii) Is ∠AOC adjacent to ∠AOE?
(iii) Do ∠COE and ∠EOD form a linear pair?
(iv) Are ∠BOD and ∠DOA supplementary?
(v) Is ∠1 vertically opposite to ∠4?
(vi) What is the vertically opposite angle of ∠5?

10. Indicate which pairs of angles are:
(i) Vertically opposite angles. (ii) Linear pairs.

11. In the following figure, is ∠1 adjacent to ∠2? Give reasons.

12. Find the values of the angles x, y, and z in each of the following:
(i) (ii)

13. 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 at a point, then the vertically opposite angles are always
_____________.
(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 __________.

14. In the adjoining figure, name the following pairs of angles.
(i) Obtuse vertically opposite angles
(iii) Equal supplementary angles
(iv) Unequal supplementary angles
(v) Adjacent angles that do not form a linear pair

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