Transcript Angles - Larose


Angle
› Formed by two rays with the same endpoint

Vertex
› The name for the common endpoint

Sides
› The rays that make up the angle

An angle can be named in a few
different ways:

With an angle symbol
and the vertex
 óA
Or using three points
 The vertex must always be in the middle!

› óBAC or
› óCAB

Or with a number on the inside of the
angle
› ó4
Interior contains all the points between
the two sides
 Exterior contains all the points outside the
angle


Between 0 and 90 degrees
xO

Exactly 90O

Between 90 and 180 degrees
xO

Exactly 180o
xO
Draw an angle on one side of paddy
paper
 Fold the paper in half


Trace the angle on the other side of the
paper
You should see two angles
 Answer Question 1 on the work sheet


Cut out one of the angles leaving the
other on the paper

Cut the separate
angle into two
different angles
through the vertex

You should now have one angle on
paper and one cut into two pieces

Place the cut angle onto the original
angle any way as long as the vertex lines
up

Answer question 2

Notice how the two pieces add up to
the one angle

Remember how two
pieces of a line add
up to the whole

If point B is in the interior of óAOC, then
óAOB + óBOC = óAOC

If óROT = 155O, what are the measures of
angles ROS and SOT?
 Remember:
(4x - 20)O
(3x + 14)O

Plug in each piece and make it equal
the total
(4x - 20)O
(3x + 14)O

Combine like terms

Add 6 to both sides

Divide by 7

If óROT = 155O, what are the measures of
angles ROS and SOT?

So if x = 23, plug it into 4x – 20 to find óROS
(4x - 20)O
(3x + 14)O

If óROT = 155O, what are the measures of
angles ROS and SOT?

So if x = 23, plug it into 3x + 14 to find óSOT
72O
(3x + 14)O

If óROT = 155O, what are the measures of
angles ROS and SOT?
 Do your answers make sense?
72O
83O

If móAMC = 140, what is x?

Find móAMB.
(3x + 17)O
(5x – 45)O

Two or more angles that have the same
measure
40O
40O
Take one piece of Patty Paper (tracing
paper)
 Draw two straight and intersecting lines


The angles don’t
matter except they
should not be 90
degrees
Label the intersection point E
 Put a point on each ray A, B, C, and D

Fold the paper at the point E so that ray
EA and ray ED line up on top of each
other
 Answer questions 1 and 2

Fold the paper at the point E so that ray
EA and ray EB line up on top of each
other
 Answer questions 3 and 4


Mark the pairs of congruent angles

Notice how the vertical
angles (across from each
other) are congruent
Two angles whose sides are opposite
rays
 Think the opposite sides of an x
 They are congruent


Two coplanar angles with a common
side, a common vertex, and no common
interior points
Angles AMB and BMC are adjacent
 Angles AMB and CMC are not!


Angles AMB and CMC are not!
› They don’t have a common side

Angles AMC and BMC are not!
› They share common point between B and C

Two angles whose measures have a sum
of 90 degrees.

Each angle is called the complement of
the other
50O
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Two angles whose measures have a sum
of 180 degrees

Each angle is called the supplement of
each other
50O

If two angles form a linear pair, then they
are supplementary
120O
60O

A ray that cuts an angle into two
congruent angles