# FIND MEASURES OF COMPLEMENTARY SUPPLEMENTARY VERTICAL AND ADJACENT ANGLES

Find measures of complementary supplementary vertical and adjacent angles :

Here we are going to discuss about complementary, supplementary, vertical adjacent and congruent angles.

## Complementary Angles

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

For example, if A = 52° and B = 38°, then angles A and B are complementary to each other. ## Supplementary Angles

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

For example, the angles whose measures are 112° and 68° are supplementary to each other. ## Vertical angles

The angles opposite each other when two lines cross. They are always equal. ∠DOB  =  ∠AOC

∠DOA  =  ∠COB

Two angles are adjacent when they have common side and common vertex  and do not overlap. Angle AOC is adjacent to angle BOC

Because:

• they have a common side (line OB)
• they have a common vertex (point O)

## Congruent angles

Congruent Angles have the same angle

• They don't have to point in the same direction.
• They don't have to be on similar sized lines.
• Just the same angle. ∠ABC  =  ∠DOE

## Vertical adjacent complementary supplementary angles-practice questions

Example 1 :

Find the value of x in the following figures Solution :

Since AOB is a straight line, the sum of these three angles will be 180 degree.

∠AOC  +  ∠COD +  ∠DOB  =  180°

∠AOC  = (x - 20)°,  ∠COD  =  x°,  ∠DOB  =  40°

(x - 20) + x + 40  =  180

2x + 20  =  180

Subtract by 20 on both sides

2x + 20 - 20  =  180 - 20

2x  =  160

Divide by 2 on both sides

2x/2  =  160/2

x  =  80

Example 2 :

For what value of x will AB and CD be parallel lines. ∠FOB and ∠OHD are corresponding angles, so they  are congruent.

∠FOB  =  ∠OHD

2x + 20  =  3x - 10

Subtract by 2x on both sides

2x - 2x + 20  = 3x - 2x - 10

20  =  x - 10

20 + 10  =  x - 10 + 10

30  =  x

Hence the value of x is 30°.

Example 3 :

For what value of x will AB and CD be parallel lines. ∠FOB and ∠OGD are interior angles, so the sum of these two angles will be 180 degree

∠FOB + ∠OGD  =  180

3x + 20 + 2x  =  180

5x + 20  =  180

Subtract by 20 on both sides

5x + 20 - 20  =  180 - 20

5x  =  160

Divide by 5 on both sides

5x/5  =  160/5

x  =  32

Example 4 :

Find the value of x. 2x + x  =  90

3x  =  90

Divide by 3 on both sides

3x/3  =  90/3

x  =  30

Example 5 :

Find the value of x in the following figures Solution :

Since AOB is a straight line, the sum of these three angles will be 180 degree.

∠AOC  +  ∠COD +  ∠DOB  =  180°

∠AOC  = (x + 30)°,  ∠COD  =  115 - x ∠DOB  =  x

x + 30 +  115 - x + x  =  180°

x + 145  =  180

Subtract by 145 on both sides

x + 145 - 145  =  180 -  145

x  =  35

Hence the value of x is 35. After having gone through the stuff given above, we hope that the students would have understood "Find measures of complementary supplementary vertical and adjacent angles".