**Find measures of complementary supplementary vertical and adjacent angles :**

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

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.

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 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

**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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