LINEAR PAIRS AND VERTICAL ANGLES

Linear Pair Theorem :

Linear pair of angles are formed when two lines intersect each other at a single point. The angles are said to be linear if they are adjacent to each other after the intersection of the two lines.

∠LAS and ∠PAS are adjacent angles.

The sum of angles of a linear pair is always equal to 180°.

Vertical Angle Theorem :

The vertical angle theorem states that the vertical angles that are formed when two lines intersect are congruent.

Problem 1 :

From the picture at the right, name the 4 sets of linear pair angles?

Solution: 

Linear pair angles :

∠1 and ∠3

∠1 and ∠2

∠4 and ∠3

∠4 and ∠2

Problem 2 :

From the picture at the right, name the 2 sets of vertical angles?

Solution:

Vertical angles :

∠1 = ∠4

∠2 = ∠3

Problem 3 :

Vertical angles are always ________.

Solution:

Vertical angles are always equal.

Problem 4 :

Linear pairs are always _____, which means they add up to _____.

Solution:

Linear pairs are always supplementary, which means they add up to 180º.

Problem 5 :

x = _____

Solution:

Here x and 63° are adjacent angles, so they add upto 180°.

x° + 63° = 180°

x = 180° - 63°

x = 117°

Problem 6 :

y = _____

Solution:

Vertical angles are always equal.

So, y = 150°

Problem 7 :

k = _____

Solution:

Here k and 103° are adjacent angles, they are supplementary.

k + 103° = 180°

k = 180° - 103°

k = 77°

Problem 8 :

a = _____

Solution:

4a + 120° = 180°

4a = 180° - 120°

4a = 60°

a = 15°

Problem 9 :

w = _____

Solution:

Vertical angles are always equal.

105° = w - 10°

w = 115°

Problem 10 :

d = _____

Solution:

(d + 13) and 95° are adjacent angle. So, they add upto 180°

95° + (d + 13)° = 180°

108° + d = 180°

d = 180° - 108°

d = 72°