# 1-5: Exploring Angle Pairs - PowerPoint PPT Presentation

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1-5: Exploring Angle Pairs. Types of Angle Pairs. Adjacent angles are two angles with a common side, common vertex, and no common interior points (next to). Vertical angles are two angles whose sides are opposite rays (across from). Types of Angle Pairs, con’t.

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1-5: Exploring Angle Pairs

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## 1-5: Exploring Angle Pairs

### Types of Angle Pairs

• Adjacent angles are two angles with a common side, common vertex, and no common interior points (next to).

• Vertical angles are two angles whose sides are opposite rays (across from).

### Types of Angle Pairs, con’t

• Complementary angles are two angles whose measures have a sum of 90.

• Each angle is the complement of the other.

• Supplementary angles are two angles whose measures have a sum of 180.

• Each angle is the supplement of the other.

### Identifying Angle Pairs

• Using the diagram, decide whether each statement is true.

• BFD and CFD are adjacent angles.

• AFB and EFD are vertical angles.

• AFE and BFC are complementary.

• AFE and CFD are vertical angles.

• DFE and BFC are supplementary.

• AFB and BFD are adjacent.

### Making Conclusions from a Diagram

• Using the diagram, which angles can you conclude are…

…congruent?

…vertical angles?

…supplementary angles?

### Making Conclusions From a Diagram

• Using the diagram, can you conclude the following:

?

?

TWQ is a right angle?

bisects ?

### Linear Pairs

• A linear pair is a pair of adjacent angles whose noncommon sides are opposite rays.

• The angles of a linear pair form a straight line.

Linear Pair Postulate: If two angles form a linear pair, then they are supplementary.

### Finding Missing Angle Measures

• KPL and JPL are a linear pair, mKPL = 2x + 24, and mJPL = 4x + 36.

• What are the measure of KPL and JPL?

### Angle Bisectors

• An angle bisector is a ray that divides an angle into two congruent angles.

• Its endpoint is at the angle vertex.

### Using an Angle Bisector

• AC bisects DAB. If mDAC = 58, what is mDAB?