Download Vertical angles

Geometry
1.6 Angle Pair Relationships
VERTICAL ANGLES
Vertical angles are two angles whose sides
form two pairs of opposite rays.
1
2
4
3
VERTICAL ANGLES
Vertical angles are congruent!!!
LINEAR PAIR
Linear pair are two adjacent angles whose
noncommon sides are opposite rays.
LINEAR PAIR
The sum of the measures of angles
that form a linear pair is 180°!!!!
Example
a)
b)
c)
d)
Are angle EOD and angle COD a linear pair?
Are angle AOB and angle BOC a linear pair?
Are angle EOD and angle AOB vertical angles?
Are angle AOE and angle COD vertical angles?
Example
The measure of angle 1 is 36 degrees. Find
the measures of the other three angles.
Example
Solve for x and y. Then find the angle
measures.
(4x + 15)
(5x + 30)
(3y + 15)
(3y - 15)
COMPLEMENTARY ANGLES
Two angles are complementary angles if the
sum of their measures is 90 degrees. Each
angle is the complement of the other.
Complementary angles can be adjacent or
nonadjacent.
SUPPLEMENTARY ANGLES
Two angles are supplementary angles if the
sum of their measures is 180 degrees. Each
angle is the supplement of the other.
Supplementary angles can be adjacent or
nonadjacent.
Example
a) Given that angle G is a supplement of angle H
and measure of angle G is 82 degrees, find
the measure of angle H.
b) Given that angle U is a complement of angle
V and measure of angle U is 73 degrees, find
the measure of angle V.
Example
Angle W and angle Z are complementary. The
measure of angle Z is five times the measure
of angle W. Find the measure of angle W.
Example
Angle T and angle S are supplementary. The
measure of angle T is half the measure of
angle S. Find the measure of angle S.