##
**Pair of Angles**

There are some pair of angles having some specific
properties. Adjacent angles, linear pair of angles, right pair of angles,
complementary angles, supplementary angles and vertically opposite angles are
some special pair of angles. let’s learn them.

###
**Adjacent Angles**

Two angles are said to be adjacent angles if they have a
common arm and common vertex.

In
the given figure, ∠AOC and ∠BOC are adjacent angles as they have a common arm OC and the
common vertex O.

Adjacent
angles never overlap with each other.

###
**Linear Pair of Angles**

If
the sum of a pair of adjacent angles is 180°, the pair is called a linear pair
of angles.

In
the given figure, ∠AOC + ∠COB = 180°. So ∠AOC and ∠COB are linear pair of angles.

###
**Right Pair of Angles**

If
the sum of a pair of adjacent angles is 90°, the pair is called a right pair of
angles.

In
the given figure, ∠AOC + ∠COB = 90°. So ∠AOC and ∠COB are right pair of angles.

###
**Complementary Angles**

Two angles are said to be complementary angles of each other if their sum is 90°.

In
the given figure, ∠ABC = 35° and ∠DBC = 55° and ∠ABC + ∠DBC = 35° + 55° =
90°. ∴ ∠ABC and ∠DBC are complementary angles.

Similarly, ∠PQR = 70° and ∠STU = 20° and ∠PQR + ∠STU = 70° + 20° = 90°. ∴ ∠PQR and ∠STU are complementary
angles.

Each
of the angle is complement of the other.

###
**Supplementary Angles**

A pair of angles whose sum is 180° are called supplementary angles.

In
the given figure, ∠AOC = 105° and ∠BOC = 75° and ∠AOC + ∠BOC = 105° + 75° =
180°. ∴ ∠AOC and ∠BOC are supplementary angles.

Similarly, ∠ABC = 35° and ∠DEF = 145° and ∠ABC + ∠DEF = 35° + 145° = 180°. ∴ ∠ABC and ∠DEF are supplementary
angles.

Each
of the angle is supplement of the other.

###
**Vertically Opposite Angles [V.O.A.]**

When
two straight line segment intersect, the angles formed opposite to each other
are called vertically opposite angles.

In
the given figure, ∠PON and ∠QOM, ∠POM and ∠NOQ are vertically opposite angles.

Similarly,
∠TOU and ∠SOV, ∠UOS and ∠VOT are also
vertically opposite angles.

###
*Workout Examples*

*Workout Examples*

*Example 1: Find the value of x in the given figure.*

*Solution: From the figure,*

*x + 75° = 180° -----------------> Linear pair of angles.*

*or, x = 180° – 75°*

*or, x = 105°*

*Example 2: Find the value of x from the given figure.*

*Solution: From the figure,*

*x + x + 40° = 90° -----------------> Right pair of angles.*

*or, 2x = 90° – 40°*

*or, 2x = 50°*

*or, x = 50°/2*

*or, x = 25°*

*Example 3: Find the values of a, b and c in the given figure.*

*Solution: From the figure,*

*a + 40° = 180° -----------------> Linear pair of angles.*

*or, a = 180° – 40°*

*or, a = 140°*

*b = 40° ------------------> Vertically opposite angles.*

*c = a ------------------> Vertically opposite angles.*

*= 140°*

*∴*

*a = 140°, b = 40° and c = 140°*

*Example 4: Find the values of x, a and b in the given figure.*

*Solution: From the figure,*

*2x + 3x = 180° -----------------> Linear pair of angles.*

*or, 5x = 180°*

*or, x = 180°/5*

*or, x = 36°*

*a = 3x ------------------> Vertically opposite angles.*

*= 3×36°*

*= 108°*

*b = 2x ------------------> Vertically opposite angles.*

*= 2×36°*

*= 72°*

*∴*

*x = 36°, a = 108° and b = 72°*

*Example 5: Find the values of x, a and b in the given figure.*

*Solution: From the figure,*

*2x – 30° = x + 20° -----------------> Vertically opposite angles.*

*or, 2x – x = 20° + 30°*

*or, x = 50°*

*a + x + 20° = 180° ------------------> Linear pair of angles.*

*or, a + 50° + 20° = 180°*

*or, a + 70° = 180°*

*or, a = 180° – 70°*

*or, a = 110°*

*b = a ------------------> Vertically opposite angles.*

*= 110°*

*∴*

*x = 50°, a = 110° and b = 110°*

*You can comment your questions or problems regarding the pair of angles here.*

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