• Angles and Their Measures

AB

C

∠ABC

A

BC

B

Two angles that share a common vertex and side but have no common interior points.

Name the Adjacent Angles

Congruent Angles:◦ Angles that have the same degree measure

M

P

N O

∠MNP∠ONP∠ONM∠MNO

∠PNO∠PNM

FE

D

C

∠EDC∠FDC∠FDE∠EDF

∠CDF∠CDE

Example 2) Name the angles in the figure.

FE

D

C

∠CDF = 62 + 18

Example 3) In the figure above, M CDE = 62o and m EDF = 18o. Find the measure of CDF.

62o 18o

∠CDF =800

Bulbs

Middle angle = 120 – 35

Example 4) The backyard of a house is illuminated by a light fixture that has two bulbs. Each bulb illuminates an angle 120o. If the angle illuminated only the right bulb is 35o, what is the angle illuminated by both bulbs?

120o

120o

= 85o

35o

Example 5) Plot the points A(-3 , -1), B (-1, 1), C(2, 4), D(2,1), and E(2,-2). Classify the following angles as acute, right, obtuse, or straight.

x

y

E

D

C

B

A

DBE EBC ABC ABDa) b) c) d)

Acute(About 45o)

Right(About 90o)

Straight(180o)

Obtuse(About 120o)

Example 6) Draw 5 points A, B, C, D and E so that all four statements are true: angles AEC and BEC are adjacent angle AEB is obtuse D is on the exterior of angle AEB Angle DEC is a right angle

A

D

B

C

E

Example 7) Angle JKL is a straight angle and JKM is 115o. H is in the interior of JKM. HKL is 130o. Find the measure of HKM

J

H

LK

M

115o

130o

= 130 - 115 HKM= 65o