Think “2 angles
that are next to
eachother with a
common side”
Think “2 sides
that form a
straight line”
a common vertex and
No common interior
Angle 3 and angle ABC
have a common interior space
Non common sides
do not form a straight
line
Non common sides
form a straight line
If they can’t be
adjacent, think
“across from
each other”.
Diagram will
always form a
perfect X shape.
Angle 3 and
angle ABC do
not
have a common
vertex.
Angle 3 and
angle 4
are also across
from eachother.
Angle 1 and angle 2
are across from eachother.
Although angles
AEB and DEC
are across from
each other, they
do not create a
perfectly
straight X.
a) ROADWAYS Name an angle
pair that satisfies the condition
two angles that form a linear
pair.
SAMPLE ANSWER:
PIQ and QIS
b) ROADWAYS Name an angle
pair that satisfies the condition
two acute vertical angles.
SAMPLE ANSWER:
PIQ and TIS
(always the same measure)
(they can be adjacent angles or non adjacent angles)
(they can be adjacent angles or non
adjacent angles. If they are adjacent,
then they are also a linear pair.)
(like angle addition!)
ALGEBRA Find the measures of two supplementary
angles if the measure of one angle is 6 less than five times
the measure of the other angle.
Watch and COPY:
Supplementary means the measure of two angles will add up to 180.
Since we don’t know what “the other angle” is, let’s call it x.
Then the first angle is 5x – 6 (six less (subtract) than 5 times (multiply) the other (x))
Use angle addition: 1 + 2 = 180
5x - 6 + x = 180
6x - 6 = 180
6x = 186
x = 31
x represents “the other angle”, so 2 = 31
 1 = 5x-6 = 5(31) – 6 = 149 so 1 = 149
Even though only one symbol is
drawn,
There are 4 right angles.
(four 90 angles)
“Line AD is perpendicular to line CB.”
Find x and y so that KO and HM
are perpendicular.
If the lines are , a right  is formed.
MJO is a right angle. Right angles equal 90.
Since mMJO = 3y + 6,
set up the following equation:
3y + 6 = 90. Solve for y.
To solve for x:
3y = 84
Another right  is formed. Look at the angles that
y = 28.
involve an x.
KJH is a right angle, but is created by adding
2 angles together.
KJI + IJH = KJH
Substitute in to set up the following equation:
3x + 6+ 9x = 90. Solve for x.
12x + 6 = 90
12x = 84
x=7
Important to READ through.
NEVER assume anything in a
picture is congruent or perpendicular.
It must be told to you in directions,
or already marked in the picture.
Determine whether the following statement can be
justified from the figure below. Explain.
a) mVYT = 90°
Yes. This is true because XYV
is marked as a right angle and creates
a linear pair with TYV.
Linear pairs add to 180. If one angle is 90
then the other angle must also be 90.
Determine whether the following statement can be
justified from the figure below. Explain.
b) TYW and TYU are supplementary.
Yes. This is true because the two given angles
form a linear pair. Linear pairs add to 180.
Supplementary angles also add to 180.
Determine whether the following statement can be
justified from the figure below. Explain.
c) VYW and TYS are adjacent angles.
No. Although they share a common vertex,
these angles do not share a common side.