Name: _______________________________
1.5: Angle Relationships
Pair-Share: Use the diagram below and a protractor to measure each angle. Answer the follow-up questions!
Find the measure of each angle:
1) m<MKS = __________
2) m<MKJ = __________
3) m<JKA = __________
4) m<SKA = __________
5) Write your angle measurements into each angle in the diagram. What pattern do you notice?
6) Compare <JKA and <SKA. How are these angles related to each other both in position and in
measurement?
7) Compare <MKS and <JKA. How are these angles related to each other both in position and in
measurement?
8) Do you think these angle relationships are always true for two intersecting lines? Why or why not?
Vocab
Definition
Diagram
Adjacent angles Two angles in the same plane with a common
vertex and side, but have no common interior
points.
Linear pair
1
2
A pair of adjacent angles whose non common
sides are opposite rays.
2
1
Two angle whose measures have a sum of
_______.
Complementary
(the angles are not always adjacent)
angles
1
2
Two angle whose measures have a sum of
_______.
Supplementary
angles
1
(the angles are not always adjacent)
Two nonadjacent angles formed by two
Vertical angles
__________________________ lines.
1
These angles are always
2
____________________.
Perpendicular
Lines
Intersecting lines that form __________
angles.
2
Practice:
1)
DEF and
both angles.
FEG are complementary. m DEF = 3x – 4 and m FEG = 5x+6. Find the measure of
Step 1: Define key word
Step 2: Draw a picture
Step 3: Write an equation!
2) <ABC and <GHI are supplementary angles. m<ABC = 8x – 2 and m<GHI = x + 20. Find the measure of
both angles.
3) Find the measure of 2 supplementary angles if the difference in the measures of the two angles is 18.
(Hint: Set one of the angles equal to “x”- our unknown)
4)
Find x. Remember, what kind of angles are these?
x
(5x-48)
5) Find x and y so that KO and HM are perpendicular.
1.1-1.4 Review
6) Find the distance between points A(-2, 5) and B(3, 4).
7) Find the midpoint of EF with endpoints E(6, 8) and F(-1, -5).
8) Find the coordinates of T if M(2, -5) is the midpoint of TW with W(-6, 1).
9) In the figure,
and
are opposite rays,
bisects ∠EBC.
a) If m∠ EBD = 4x + 16 and m∠ DBC = 6x + 4, find m∠ EBD.
b) If m∠ EBD = 4x - 8 and m∠ EBC = 5x + 20, find the value of x and m∠ EBC.
Homework:
p.51-52 #8, 14, 16, 19-25 odd, 29