1. SECTION 4-2
Angles ofTriangles

2. ESSENTIAL QUESTIONS
• How do you apply theTriangle Angle-SumTheorem?
• How do you apply the Exterior AngleTheorem?

3. VOCABULARY
1.Auxiliary Line:
2. Exterior Angle:
3. Remote Interior Angles:
4. Flow Proof:

4. VOCABULARY
1.Auxiliary Line: An extra line or segment that is added to
a figure to help analyze geometric relationships
2. Exterior Angle:
3. Remote Interior Angles:
4. Flow Proof:

5. VOCABULARY
1.Auxiliary Line: An extra line or segment that is added to
a figure to help analyze geometric relationships
2. Exterior Angle: Formed outside a triangle when one side
of the triangle is extended;The exterior angle is adjacent
to the interior angle of the triangle
3. Remote Interior Angles:
4. Flow Proof:

6. VOCABULARY
1.Auxiliary Line: An extra line or segment that is added to
a figure to help analyze geometric relationships
2. Exterior Angle: Formed outside a triangle when one side
of the triangle is extended;The exterior angle is adjacent
to the interior angle of the triangle
3. Remote Interior Angles: The two interior angles that are
not adjacent to a given exterior angle
4. Flow Proof:

7. VOCABULARY
1.Auxiliary Line: An extra line or segment that is added to
a figure to help analyze geometric relationships
2. Exterior Angle: Formed outside a triangle when one side
of the triangle is extended;The exterior angle is adjacent
to the interior angle of the triangle
3. Remote Interior Angles: The two interior angles that are
not adjacent to a given exterior angle
4. Flow Proof: Uses statements written in boxes with
arrows to show a logical progression of an argument

8. THEOREMS & COROLLARIES
4.1 -Triangle Angle-SumTheorem:
4.2 - Exterior AngleTheorem:
4.1 Corollary:
4.2 Corollary:

9. THEOREMS & COROLLARIES
4.1 -Triangle Angle-SumTheorem: The sum of the
measures of the angles of any triangle is 180°
4.2 - Exterior AngleTheorem:
4.1 Corollary:
4.2 Corollary:

10. THEOREMS & COROLLARIES
4.1 -Triangle Angle-SumTheorem: The sum of the
measures of the angles of any triangle is 180°
4.2 - Exterior AngleTheorem: The measure of an exterior
angle of a triangle is equal to the sum of the measures of
the two remote interior angles
4.1 Corollary:
4.2 Corollary:

11. THEOREMS & COROLLARIES
4.1 -Triangle Angle-SumTheorem: The sum of the
measures of the angles of any triangle is 180°
4.2 - Exterior AngleTheorem: The measure of an exterior
angle of a triangle is equal to the sum of the measures of
the two remote interior angles
4.1 Corollary: The acute angles of a right triangle are
complementary
4.2 Corollary:

12. THEOREMS & COROLLARIES
4.1 -Triangle Angle-SumTheorem: The sum of the
measures of the angles of any triangle is 180°
4.2 - Exterior AngleTheorem: The measure of an exterior
angle of a triangle is equal to the sum of the measures of
the two remote interior angles
4.1 Corollary: The acute angles of a right triangle are
complementary
4.2 Corollary: There can be at most one right or obtuse
angle in a triangle

13. EXAMPLE 1
The diagram shows the paths a ball is thrown in a game
played by kids. Find the measure of each numbered angle.

14. EXAMPLE 1
The diagram shows the paths a ball is thrown in a game
played by kids. Find the measure of each numbered angle.
m∠1=180 − 43− 74

15. EXAMPLE 1
The diagram shows the paths a ball is thrown in a game
played by kids. Find the measure of each numbered angle.
m∠1=180 − 43− 74 = 63°

16. EXAMPLE 1
The diagram shows the paths a ball is thrown in a game
played by kids. Find the measure of each numbered angle.
m∠1=180 − 43− 74 = 63°
m∠2

17. EXAMPLE 1
The diagram shows the paths a ball is thrown in a game
played by kids. Find the measure of each numbered angle.
m∠1=180 − 43− 74 = 63°
m∠2 = 63°

18. EXAMPLE 1
The diagram shows the paths a ball is thrown in a game
played by kids. Find the measure of each numbered angle.
m∠1=180 − 43− 74 = 63°
m∠2 = 63°
m∠3 =180 − 63− 79

19. EXAMPLE 1
The diagram shows the paths a ball is thrown in a game
played by kids. Find the measure of each numbered angle.
m∠1=180 − 43− 74 = 63°
m∠2 = 63°
m∠3 =180 − 63− 79 = 38°

20. EXAMPLE 2
Find m∠FLW.

21. EXAMPLE 2
Find m∠FLW.
m∠FLW = m∠LOW + m∠OWL

22. EXAMPLE 2
Find m∠FLW.
m∠FLW = m∠LOW + m∠OWL
2x − 48 = x + 32

23. EXAMPLE 2
Find m∠FLW.
m∠FLW = m∠LOW + m∠OWL
2x − 48 = x + 32
x − 48 = 32

24. EXAMPLE 2
Find m∠FLW.
m∠FLW = m∠LOW + m∠OWL
2x − 48 = x + 32
x − 48 = 32
x = 80

25. EXAMPLE 2
Find m∠FLW.
m∠FLW = m∠LOW + m∠OWL
2x − 48 = x + 32
x − 48 = 32
x = 80
m∠FLW = 2(80)− 48

26. EXAMPLE 2
Find m∠FLW.
m∠FLW = m∠LOW + m∠OWL
2x − 48 = x + 32
x − 48 = 32
x = 80
m∠FLW = 2(80)− 48 =160 − 48

27. EXAMPLE 2
Find m∠FLW.
m∠FLW = m∠LOW + m∠OWL
2x − 48 = x + 32
x − 48 = 32
x = 80
m∠FLW = 2(80)− 48 =160 − 48 =112°

28. EXAMPLE 3
Find the measure of each numbered angle.

29. EXAMPLE 3
Find the measure of each numbered angle.
m∠5 =180 − 90 − 41

30. EXAMPLE 3
Find the measure of each numbered angle.
m∠5 =180 − 90 − 41 = 49°

31. EXAMPLE 3
Find the measure of each numbered angle.
m∠5 =180 − 90 − 41 = 49°
m∠3 = 90 − 48

32. EXAMPLE 3
Find the measure of each numbered angle.
m∠5 =180 − 90 − 41 = 49°
m∠3 = 90 − 48 = 42°

33. EXAMPLE 3
Find the measure of each numbered angle.
m∠5 =180 − 90 − 41 = 49°
m∠3 = 90 − 48 = 42°
m∠4 =180 − 90 − 42

34. EXAMPLE 3
Find the measure of each numbered angle.
m∠5 =180 − 90 − 41 = 49°
m∠3 = 90 − 48 = 42°
m∠4 =180 − 90 − 42 = 48°

35. EXAMPLE 3
Find the measure of each numbered angle.
m∠5 =180 − 90 − 41 = 49°
m∠3 = 90 − 48 = 42°
m∠4 =180 − 90 − 42 = 48°
90 − 34

36. EXAMPLE 3
Find the measure of each numbered angle.
m∠5 =180 − 90 − 41 = 49°
m∠3 = 90 − 48 = 42°
m∠4 =180 − 90 − 42 = 48°
90 − 34
m∠2 =180 − 56 − 48

37. EXAMPLE 3
Find the measure of each numbered angle.
m∠5 =180 − 90 − 41 = 49°
m∠3 = 90 − 48 = 42°
m∠4 =180 − 90 − 42 = 48°
90 − 34 = 56
m∠2 =180 − 56 − 48

38. EXAMPLE 3
Find the measure of each numbered angle.
m∠5 =180 − 90 − 41 = 49°
m∠3 = 90 − 48 = 42°
m∠4 =180 − 90 − 42 = 48°
90 − 34 = 56
m∠2 =180 − 56 − 48 = 76°

39. EXAMPLE 3
Find the measure of each numbered angle.
m∠5 =180 − 90 − 41 = 49°
m∠3 = 90 − 48 = 42°
m∠4 =180 − 90 − 42 = 48°
90 − 34 = 56
m∠2 =180 − 56 − 48 = 76°
m∠1=180 − 76

40. EXAMPLE 3
Find the measure of each numbered angle.
m∠5 =180 − 90 − 41 = 49°
m∠3 = 90 − 48 = 42°
m∠4 =180 − 90 − 42 = 48°
90 − 34 = 56
m∠2 =180 − 56 − 48 = 76°
m∠1=180 − 76 =104°

41. EXAMPLE 3
Find the measure of each numbered angle.
m∠5 =180 − 90 − 41 = 49°
m∠3 = 90 − 48 = 42°
m∠4 =180 − 90 − 42 = 48°
90 − 34 = 56
56°
m∠2 =180 − 56 − 48 = 76°
m∠1=180 − 76 =104°

42. PROBLEM SET

43. PROBLEM SET
p. 248 #1-37 odd, 46, 57
“We rarely think people have good sense unless they
agree with us.” - Francois de La Rochefoucauld