FIND MEASURES OF COMPLEMENTARY SUPPLEMENTARY VERTICAL AND ADJACENT ANGLES

About "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

Adjacent angles 

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

Add 10 on both sides

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.

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