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 diagram shown below.

**Solution :**

**Because all the three angle measures in the above diagram are on the same straight line AOB, they are supplementary. **

**(x - 20)****° + ****x****° + ****40**° = 180**°**

**x - 20 + x + 40 = 180**

**2x + 20 = 180**

**Subtract 20 from each side. **

**2x = 160**

Divide each side by 2.

x = 80

**Problem 2 :**

In the diagram shown below, if the lines AB and CD are parallel and EF is transversal, find the value of 'x'.

**In the diagram shown above, because the lines AB and CD are parallel and EF is transversal, ∠FOB and ****∠OHD are corresponding angles and they are congruent.**

**Then,**

**∠FOB = ****∠OHD**

**(2x + 20)****°**** = (3x - 10)****°**

**2x + 20 = 3x - 10**

**Subtract 2x from each side.**

**20 = x - 10**

**Add 10 to each side.**

**30 = x**

**Problem 3 :**

In the diagram shown below, if the lines AB and CD are parallel and EF is transversal, find the value of 'x'.

**In the diagram shown above, because the lines AB and CD are parallel and EF is transversal, ****∠BOG and ****∠OGD are consecutive interior angles and they are supplementary.**

**Then, **

**∠BOG + ****∠OGD = 180****°**

**(3x + 20)****°**** + 2x****°**** = 180****°**

**3x + 20 + 2x = 180**

**5x + 20 = 180**

**Subtract 20 from each side. **

**5x = 160**

**Divide each side by 5.**

**x = 32**

**Problem 4 :**

Find the value of 'x' in the diagram shown below.

In the diagram shown below, it clear that the angle measures x**° and (2x)****° are complementary. **

**Then, **

(2x)**° + x****° = 90****°**

2x + x = 90

3x = 90

Divide each side by 3.

x = 30

**Problem 5 :**

Find the value of 'x' in the diagram shown below.

**Solution :**

**Because all the three angle measures in the above diagram are on the same straight line AOB, they are supplementary. **

**Then,**

**(x + 30)****° + (****115 - x)****° + ****x****° = 180****°**

**x + 30**** + 115 - x + x = 180**

**x + 145 = 180**

**Subtract 145 from each side. **

**x = 35**

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