Download Exterior Angle Remote Interior Angles

LINE AND ANGLE RELATIONSHIPS
10.2 Interior and Exterior Angles
Angle Sum of a Triangle
Concept: The sum of the measure of the _________ angles
Exterior Angles of a Triangle
Concept: The measure of an __________ angle of a
of a triangle is equal to _______.
triangle is equal to the sum of the measures of its two
remote __________ angles.
2
2
1
3
1
Angle 1 + Angle 2 + Angle 3 = _______
3
4
Angle 4 is an _________ angle.
Examples
A)
Find the value of x in the Antigua and Barbuda flag.
Angle 1 and Angle 2 would be the _______________ angles.
Angle ___ + Angle ___ = Angle ___
x°
Something to think about… Angle 3 and Angle 4 make a
straight angle. They must also equal _____.
55°
x + ____ + ____ = 180
Examples
A)
Suppose m<4 = 135°. Find the measure of <1.
x + _____ = 180
1
B) In triangle ABC, if angle A = 72° and angle B = 74°, what is
the measurement of angle C?
3
4
Angle 4 is an exterior angle. Its two remote interior angles are
<1 and <2 (the right angle).
m<1 + m<2 = m<4
x + ___ = _____
TRIANGLE CARDS
FILL IN THE INFORMATION
The sum of the
angles in a triangle
is 180.
a + b + c = 180
TRIANGLE UNKNOWNS
?
X
find x
45°
180-90-45
45°
X
X
3x = 180
3x = 180
3
3
x = 60°
2x + 3x + 4x = 180
9x = 180
9x = 180
9
9
x = 20
?
What is the above angle measure?
Lets keep this in mind 
?
Triangle Angle Names
Remote
Interior
Angles
Exterior
Angle
FYI Another Name for Remote Interior Angles are:
Non-adjacent Angles
TRIANGLE CARDS
FILL IN THE INFORMATION
The sum of the
Remote Interior
Angles equal the
measure of the
Exterior Angle.
a+b=d
TRIANGLE UNKNOWNS
45°
57°
?
45 + 90 = ?
135°
?
?
63°
120°
? + 57 = 120
? + 57 = 120
- 57 -57
? = 63°
63
2x + 3x = 105
5x = 105
5x = 105
5
5
x = 21
10.2 Interior and Exterior Angles
Day 1 – Integer operations, PEMDAS, evaluating
find x:
x + 62 = 139
x
x + 62 = 139
- 62 - 62
x = 77°
139°
62°
Number 13 on your Homework
RECAP
The sum of the
angles in a triangle
is 180.
The sum of the Remote
Interior Angles equal the
measure of the Exterior Angle.
a + b + c = 180
a+b=d
?
SIMILARITY THEOREM
When figures get bigger,
do the angles get bigger?
A’
A
Sides get bigger . . .
but ANGLES DON’T!
If you had 2 triangles with the same angle measures,
would the triangles be similar?
125
30
125
25
30
25
?
SIMILARITY THEOREM
SAME ANGLES
SAME SHAPE!
What’s the MINIMUM number of angles
you need to know to determine
if 2 triangles are similar???
125
125
25
IF 2 angles are congruent
25
‘s are SIMILAR
Are These Triangles Similar?
𝑌𝐸𝑆: ∆𝐴𝐵𝐶 ~ ∆𝐷𝐸𝐹
Similarity Recap
If 2 angles are ≅ (𝑐𝑜𝑛𝑔𝑟𝑢𝑒𝑛𝑡)
‘s are SIMILAR
∆𝐴𝐵𝐶 ~ ∆𝐷𝐸𝐹