Download topic 2-2: special angle pairs

TOPIC 3-2: SPECIAL ANGLE PAIRS
TERM
DEFINITION
Perpendicular
Lines
SKETCH
Lines that intersect to form 4
right angles.
EXAMPLE 1 NP and QR are perpendicular lines intersecting at O.
Find the value of ‘x’.
N
(5x – 5)
O
Q
R
P
Not all intersecting lines form right angles, but they do form four angles
that have special relationships.
TERM
DEFINITION
Vertical
Angles
Two non-adjacent angles
formed by intersecting lines.
Linear
Pair
Adjacent angles whose noncommon sides are opposite
rays.
SKETCH
VERTICAL ANGLES are always _____________________.
EXAMPLE 2 AC and DE intersect at B. Find the value of ‘x’ and
the measure of EBA.
A
(2x + 20)
E
B
(3x + 15)
D
C
The sum of the measures of the angles in a LINEAR PAIR is ______.
EXAMPLE 3 LN and OP intersect at M. Find the value of ‘x’ and
the measures of LMO and OMN.
O (5x + 10)
N
(7x + 20)
L
P
M
EXAMPLE 4 GH and JK intersect at I. Find the value of ‘x’ and
the measure of JIH.
G
(16x – 20)
K
J
I
(13x + 7)
H
The sum of the measures of LMO and OMN in EXAMPLE 4 is
180°. Two angles whose measures have a sum of 180 are called
_______________________________.
Similarly, when the sum of the measures of two angles is 90°, the
angles are called _________________________________.
EXAMPLE 5 If 1 and 2 are complements, with m1 = (2x + 20)
and m2 = (3x + 15), find the value of ‘x’.
EXAMPLE 6 Find all of the missing angles.
m1 = __________
m2 = __________
110
m3 = __________
45 2
1
4
3
m 4 = __________
EXAMPLE 7 CD  AB, m1 = (6x – 3), m2 = (7x – 11). Find the
value of ‘x’.
A
2
C
1
D
B