Download Chapter 1 – Elements of Geometry Lesson 1.5 – Angle

Chapter 1 – Elements of Geometry
Lesson 1.5 – Angle Relationships
Adjacent Angles: Two angles that lie in the same plane, have a
common vertex and a common side, but no common interior points.
Vertical Angles: Two nonadjacent angles formed by two intersecting
lines.
Linear Pair: A pair of adjacent angles with noncommon sides that are
opposite rays.
Lesson 1.5 – Page 1
Example 1 – Identify Angle Pairs
A. Name two angles that form a linear pair.
VZY &
XZW
B. Name two acute vertical angles.
VZY &
XZW
NOW TRY THIS: Name an angle or angle pair that
satisfies the given condition.
QHG & THP
QHT & RHP
b. a pair of obtuse vertical angles
c. a linear pair whose vertices are at T
STH & PTH
a. a pair of acute vertical angles
Lesson 1.5 – Page 2
Put in terms of x for each: x & (90 – x) are complements and
x & (180 – x) are supplements.
Example 2: Find the measure of two supplementary angles if the of measure of
one angle is 6 less than five times the measure of the other ang
Let x = 1st angle
(180 - x) = 2nd angle
x 5(180 x) 6
x 900 5 x 6
6 x 894
x 149 The two angles are 149o and 31o .
NOW TRY THIS: Find the measure of two complementary angles if one angle
measures six degrees less than five times the measure of the other.
Let x = 1st angle
(90 - x) = 2nd angle
x 5(90 - x) - 6
x 450 - 5 x - 6
6 x 444
x
74
Lesson 1.5 – Page 3
The two angles are 74o and 16o .
Example 3: Find x so that KO HM .
3 x 6 9 x 90
12 x 6 90
12 x 84
x
7
Example 4: Determine whether each statement can be justified from the figure
below. Explain.
A. m VYT
90
No, Can’t assume any angles are congruent.
B.
TYW and
TYU are supplementary.
Yes, they form a linear pair.
C.
VYW and
TYS are adjacent angles. No, they do not have a common side.
Lesson 1.5 – Page 4