## Adjacent Angles

- Adjacent Angles are two angles with a shared side and a common vertex.
- For example, in the diagram shown below, $\angle ABD$ and $\angle DBC$ are adjacent angles.

- If the sum of a pair of adjacent angles is $90\xb0$, then they are complementary to each other.
- If the sum of a pair of adjacent angles is $180\xb0$, then they are supplementary to each other.

## Vertical Angles

- The pairs of
**opposite**angles formed by intersecting lines are called Vertical Angles or Vertically Opposite Angles. - For example, in the diagram shown below, $\angle a$ and $\angle b$ are vertical angles, and so are $\angle c$ and $\angle d$.

- Vertical angles are always congruent. Hence, in the diagram above $m\angle a=m\angle b$, and $m\angle c=m\angle d$.

## Solved Examples

Question 1: Find the measure of $\angle AOD$, if $\angle BOC=125\xb0$.

Solution: $\angle AOD=\angle BOC$ $\left\{\text{verticalangles}\right\}$

$\angle AOD=125\xb0$

Question 2: In the figure shown below, find the measure of $\angle ABD$.

Solution: $\angle ABD=\angle ABC+\angle CBD$$=50\xb0+40\xb0$$=90\xb0$

## Cheat Sheet

- Two angles having the same vertex and a common side between them are called Adjacent Angles.
- A pair of adjacent angles can be complementary or supplementary angles.
- Vertical angles are pairs of opposite angles formed by intersecting lines.
- Vertical angles are always equal in measure.

## Blunder Areas

- Vertical angles always are congruent.
- Vertical angles cannot be adjacent angles.
- Congruent angles have the same degree measure.

- Fiona Wong
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