Download TOPIC 2-2: SPECIAL ANGLE PAIRS

TOPIC 3-2: SPECIAL ANGLE PAIRS (textbook 1-4)
PERPENDICULAR LINES: 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)
Q
O
R
P
Supplementary Angles: two angles whose measures have a
sum of 180
Complementary Angles: two angles whose measures have a
sum of 90
EXAMPLE 2 If 1 and 2 are complements, with m1 = (2x + 20)
and m2 = (3x + 15), find the value of ‘x’.
ADJACENT ANGLES: angles that have a common vertex and side, but
no common interior points.
When 2 lines intersect, they form four angles that have special
relationships.
4
NAME
DESCRIPTION
1
3
2
EXAMPLES
Adjacent angles whose noncommon sides are opposite
rays.
Linear
Pair
Linear Pair Theorem:
The 2 angles in a linear pair are
always supplementary.
2 non-adjacent angles formed
by 2 intersecting lines.
Vertical
Angles
Vertical Angles Theorem:
Vertical angles are always
congruent.
EXAMPLE 3 AC and DE intersect at B. Find the measure of
DBC and the measure of EBC.
A
93
E
B
D
C
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
EXAMPLE 5 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 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