Download Example 1 - Campbell County Schools

Angle Measures
LT – I can find and compare angle measures.
Definition of an Angle
Angle – formed by two rays with the same endpoint. The rays are the sides or
legs of the angle and the endpoint is the vertex.
vertex
A. Naming an Angle
The name can be the number between the sides of the angle: / 3.
The name can be the vertex of the angle: / G.
The name can be three points that include on each ray with the vertex
written in the middle/ AGC, / CGA.
Example 1: Name all the angles
/1
/ ABC
/F
Example 2: Name the Adjacent Angles
These angles are called “adjacent”
which means “next to” because
they share a ray.
/ POR & / ROQ
NOT / ORQ , / ORP, or /O
B. Classifying Angles
Acute < 90
Obtuse > 90
Right = 90
Straight = 180
State whether the following are acute, right, or obtuse.
1.
acute
3.
right
2.
4.
?
?
acute
5.
obtuse
obtuse
C. Angle Addition Postulate
Example 1 Suppose that m/1 = 42 and m/ ABC = 88. Find m/2.
88°
42°
m /1 + m /2 = m/ ABC
42 + m/2 = 88
m/2 = 46
Angle Addition Postulate.
Substitute 42 for m/1 and 88 for m/ABC.
Subtract 42 from each side.
Example 2 If m/RQT = 155, what are m/RQS and m/TQS?
(4x – 20) + (3x + 16) = 155
7x – 6 = 155
7x = 161
x = 23
m/RQS =
=
=
=
4x – 20
4(23) – 2 0
92 – 20
72
m/TQS = 3x + 14
= 3(23) + 14
= 69 + 14
= 83
Combine like terms.
Add 6 to each side
Divide each side by 7.
D. Congruent Angles
Angles with the same measure are congruent. Congruent angles
are marked by arcs.
For example …
130°
/CBJ
/DHG
If m /GHF = 130, then,
m /JBC = 130
130°
When we use a protractor, we need to
line it up correctly.
You need to make sure the protractor is lined up correctly.
Is this ready to measure the angle?
Were you right......................it wasn’t
Look for the upside down ‘T’ in the middle of
the straight line on your protractor.
This needs to be exactly on the vertex of
your angle.
We need to remember.....
It doesn’t
matter which
way round the
angle is, you
ALWAYS need
to line the upside
down ‘T’ to the vertex
of the angle.
Now you are ready.
Read from the 0°, and follow the inner set of
numbers.
Once you reach 30° you need to be
careful!!!
You then need to look at the 1° markings on
the outer set of numbers.
What does it measure?
This angle measures 35°.