1.6 measuring angles to find the measures of angles to identify special angle pairs

1.6 Measuring Angles• To Find the Measures of Angles• To Identify Special Angle Pairs

What is an Angle?

• An Angle () is formed by two rays that share the same endpoint.• The rays are the sides

of the angle.• Here Ray BT and Ray

BQ meet at the vertex of the angle, which is B.

Naming an Angle…

We can name this Angle…

• By its vertex: • < B (Angle B)

• By using three points:• < TBQ (Angle TBQ)• < QBT (Angle QBT)

• By a Number: • < 1 (Angle One)

Naming Angles

• Name <1 in two other ways.• < AEC • <CEA

• Name <CED in two other ways.• < 2 • <DEC

• Can we name any of the angles <E? Why or Why not?

Example 1A

a. Give Two other names for <ABD.

b. Which 3 Angles have D as their Vertex?

Example 1B

c. Does <3 and <Z name the same Angle? Explain.

d. List all the angles that have W as a Vertex.

Classifying Angles by their Measures

Classifying Angles by their Measures

Congruent Angles…• Angles with the same measures are Congruent Angles. • In other words…• If then

Angle Addition Postulate…

Ex 2: Using the Angle Addition Postulate

a. What is m<TSW if m<RST = 50 and m<RSW = 125?

Ex 2B: Try one…

If m<DEG = 145, find m<GEF.(Remember m<DEF=180 because it’s a Straight Angle)

Ex 3: Some More Algebra…c. In the figure, ray XP and ray XT are opposite rays and ray XQ

bisects <PXS. For each situation, find the value of x and the measure of the indicated angle.

Ex 3: Some More Algebra…

d. Find m<RXS.

Identifying Angle Pairs…

Example 4

Tell whether each pair of angles are only adjacent, adjacent and form a linear pair, or not adjacent.

a. <AEB and <BED b. <AEB and <BECc. <DEC and <AEB

Identifying Angle Pairs…

Identifying Angle Pairs…

Ex 5: Identify Angle Pairs

Ex 6: Find The Measure…

Find:

a) complement of <F b) supplement of <F

Ex 7: Find x!

What can I assume from a diagram?

If you are given a diagram, there are some ideas we can conclude just by looking at it.

You can conclude that angles are:• Adjacent• Adjacent Supplementary• Vertical• Straight

What can’t I assume from a Diagram?

Unless there are marks or symbols indicated in the diagram, you cannot assume that:• Angles or segments are congruent• Angles are Right or 90 degrees• Lines are Parallel or Perpendicular

Make Conclusions…

Ex 8: Can you make these conclusions?

Closure…• How are angles

classified?• What are the special

Angle pairs?