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

**Problem 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**

**Problem 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****°.**

**Problem 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**

**Problem 4 :**

Find the value of x.

2x + x = 90

3x = 90

Divide by 3 on both sides

3x/3 = 90/3

x = 30

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