Angle Relationships

90 and 180 degree angles……

• 90 degree angle:• 180 degree angle:

Types of angles……• Acute – angles less than 90 degrees.• Right – angles with exactly 90

degrees.

• Obtuse – angles greater than 90 degrees but less than 180 degrees.

• Straight – angles that are 180 degrees and form a line.

Identify these angles…..• A.

• B.

• C.

• D.

• A. Obtuse

• B. Right

• C. Acute

• D. Straight

Adjacent Angles……• Two angles that share a common side

are adjacent angles.

• Example:

Non-adjacent Angles……• Angles that do not share a common

side are non-adjacent angles.

• Example:

Supplementary• Two angles whose sum is 180.

Complementary• Two angles whose sum is 90.

Perpendicular• If 2 segments are perpendicular to

each other, then they form a 90 degree angle.

• The symbol for perpendicular is an upside down T.

• Example:

.90

2,toupaddmust

anglestheTherefore

kj

Let’s finish this problem...Remember that

.angleeach

ofvaluetheandxFind

kj

30

903

902

x

x

xx

30

603022 x

60

Find x, given that gf

11

555

90355

9025105

x

x

x

x

Vertical Angles……• Vertical Angles are two non-adjacent

angles formed by intersecting lines.

• Vertical Angles are congruent. (Equal)

43,

.43

21,

.21

mmSo

anglesverticalareand

mmSo

anglesverticalareand

Example……• Find the value of x.

63

685

x

x

Example…..• Find the PQRm

12

242

24810

x

x

xx

120)12(1010 xPQRm

Linear Pairs

Linear Pair – a pair of adjacent angles whose non-common sides form opposite rays.

1 2

∠1 and ∠2 form a linear pair.

A linear pair is supplementary – the angle measuresadd up to 180 degrees.

Find x:

30

1806

1805

x

x

xx

Homework• Angle Relationships Worksheet