The document discusses the exterior angle theorem, which states that the measure of an exterior angle of a triangle is equal to the sum of the remote interior angles and is greater than either of the remote interior angles. It defines key terms such as exterior angle, interior angle, remote interior angle, and provides examples of applying the exterior angle theorem and exterior angle inequality theorem to solve problems about angle measures in triangles.

1. Exterior Angle TheoremExterior Angle Theorem
You will learn to identify exterior angles and remote interior
angles of a triangle and use the Exterior Angle Theorem.
1) Interior angle
2) Exterior angle
3) Remote interior angle

2. Exterior Angle TheoremExterior Angle Theorem
1
2 3 4
P
Q R
interior
Angle 4 is called an _______ angle of ΔPQR.exterior
An exterior angle of a triangle is an angle that forms a _________ with one of
the angles of the triangle.
linear pair
____________________ of a triangle are the two angles that do not form
a linear pair with the exterior angle.
Remote interior angles

3. Exterior Angle TheoremExterior Angle Theorem
1
2
3 4 5
In the figure below, ∠ 2 and ∠ 3 are remote interior angles with respect to
what angle? ∠ 5

4. Exterior Angle TheoremExterior Angle Theorem
Theorem 7 – 3
Exterior
Angle
Theorem
The measure of an exterior angle of a triangle is equal to sum
of the measures of its ___________________.remote interior angles
X
432
1
ZY
m ∠ 4 =m ∠ 1 + m ∠ 2

5. Exterior Angle TheoremExterior Angle Theorem

6. Exterior Angle TheoremExterior Angle Theorem
Theorem 7 – 4
Exterior
Angle
Inequality
Theorem
The measure of an exterior angle of a triangle is greater than
the measures of either of its two ____________________.remote interior angles
X
432
1
ZY
m ∠ 4 > m ∠ 1
m ∠ 4 > m ∠ 2

7. Exterior Angle TheoremExterior Angle Theorem
∠ 1 and ∠ 3
74°
1 3
2
Name two angles in the triangle below that have measures less than 74°.
Theorem 7 – 5
If a triangle has one right angle, then the other two angles
must be _____.acute

8. Exterior Angle TheoremExterior Angle Theorem
3and1 ∠∠

9. Exterior Angle TheoremExterior Angle Theorem
The feather–shaped leaf is called a pinnatifid.
In the figure, does x = y? Explain.
x = y
?
__ + 81 = 32 + 7828
28°
109 = 110
No! x does not equal y

10. Exterior Angle TheoremExterior Angle Theorem
The feather–shaped leaf is called a pinnatifid.
In the figure, does x = y? Explain.
x = y
?
__ + 81 = 32 + 7828
28°
109 = 110
No! x does not equal y