1-5: Exploring Angle Pairs

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?

…adjacent angles?

…supplementary angles?

Making Conclusions From a Diagram

• Using the diagram, can you conclude the following:

? ?

TWQ is a right angle? bisects ?

TW WVPW WQ

TV PQ

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, mKPL = 2x + 24, and mJPL = 4x + 36.

• What are the measure of KPL and JPL?

ABC and DBC are a linear pair.mABC = 3x + 19 and mDBC = 7x – 9. What are the measures of ABC and DBC?

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 mDAC = 58, what is mDAB?