Download 1.5 Exploring Angle Pairs

Objective:
Students will identify and use special pairs of
angles and perpendicular lines.

Adjacent angles are
two angles that lie in
the same plane, have
a common vertex,
and a common side,
but no common
interior point.
1
2
3
4

Vertical angles are
two nonadjacent
angles formed by two
intersecting lines
4
3

Vertical angles are
ALWAYS congruent
1
2
Angles 1 and 3 are vertical;
Angles 2 and 4 are vertical.


A linear pair is a pair
of adjacent angles
whose noncommon
sides are opposite
rays.
Linear pairs have a
sum of 180 degrees.
2
1
Angles 1 and 2 form a linear pair


Complementary
angles are 2 angles
whose measures
have a sum of 90
degrees
Complementary
angles can be
adjacent or
nonadjacent
200
700


520
1280
Supplementary
angles are 2 angles
whose measures
have a sum of 180
degrees.
Supplementary
angles can be
adjacent or
nonadjacent.




Perpendicular lines
intersect to form 4 right
angles
Perpendicular lines
intersect to form
congruent adjacent angles
Segments and rays can be
perpendicular to lines or
other segments and rays
The right angle symbol in
the figure indicates the
lines are perpendicular


Lines p and q intersect to form adjacent
angles 1 and 2.
If m<1 = -3x+18 and m<2 = 8y-70, find
the values of x and y so that p is
perpendicular to q. X = -24, y = 20
The measure of angle 1 is five less than four
times the measure of angle 2. If angle 1 and
2 form a linear pair, what are their
measures? 37, 143





If m<A = 75, what are the complement and
supplement of <A? C = 15, S = 105
m<B = x. Name the complement and supplement
of <B. C = 90-x, S = 180-x
The supplement of an angle is twice the measure of
the angle. Find the angle and its supplement. 60, 120
The difference between the measures of 2
supplementary angles is 42 degrees. Find the
angles. 69, 111
A supplement of an angle is 6 times as large as the
complement of the same angle. Find the angles.
72, C = 18, S = 108