1. LESSON 4–2
Angles of Triangles

2. Five-Minute Check (over Lesson 4–1) TEKS Then/Now New Vocabulary
Theorem 4.1: Triangle Angle-Sum Theorem
Proof: Triangle Angle-Sum Theorem
Example 1: Real-World Example: Use the Triangle Angle-Sum Theorem
Theorem 4.2: Exterior Angle Theorem
Proof: Exterior Angle Theorem
Example 2: Real-World Example: Use the Exterior Angle Theorem
Corollaries: Triangle Angle-Sum Corollaries
Example 3: Find Angle Measures in Right Triangles
Lesson Menu

3. Classify ΔRST . A. acute B. equiangular C. obtuse D. right
5-Minute Check 1

4. Find y if ΔRST is an isosceles triangle with RS  RT.
___
A. 8
B. 10
C. 12
D. 14
5-Minute Check 2

5. Find x if ΔABC is an equilateral triangle.
5-Minute Check 3

6. A. ΔABC
B. ΔACB
C. ΔADC
D. ΔCAB
5-Minute Check 4

7. Classify ΔMNO as scalene, isosceles, or equilateral if MN = 12, NO = 9, and MO = 15.
A. scalene
B. isosceles
C. equilateral
5-Minute Check 5

8. Which is not a classification for ΔFGH?
A. acute
B. scalene
C. isosceles
D. equiangular
5-Minute Check 6

9. Mathematical Processes G.1(D), G.1(F)
Targeted TEKS
G.6(D) Verify theorems about the relationships in triangles, including proof of the Pythagorean Theorem, the sum of
interior angles, base angles of isosceles triangles, midsegments, and medians, and apply these relationships to
solve problems.
Mathematical Processes
G.1(D), G.1(F)
TEKS

10. You classified triangles by their side or angle measures.
Apply the Triangle Angle-Sum Theorem.
Apply the Exterior Angle Theorem.
Then/Now

11. remote interior angles flow proof corollary
auxiliary line
exterior angle
remote interior angles
flow proof
corollary
Vocabulary

12. Concept 1

13. Concept 2

14. Use the Triangle Angle-Sum Theorem
SOFTBALL The diagram shows the path of the softball in a drill developed by four players. Find the measure of each numbered angle.
Analyze Examine the information in the diagram. You know the measures of two angles of one triangle and only one measure of another. You also know that 1 and 2 are vertical angles.
Example 1

15. Triangle Angle-Sum Theorem
Use the Triangle Angle-Sum Theorem
Formulate Find m1 first because the measure of two angles of the triangle are known. Use the Vertical Angles Theorem to find m2. Then you will have enough information to find the measure of 3.
Determine
Triangle Angle-Sum Theorem
Simplify.
Subtract 117 from each side.
Example 1

16. 1 and 2 are congruent vertical angles. So, m2 = 63.
Use the Triangle Angle-Sum Theorem
1 and 2 are congruent vertical angles. So, m2 = 63.
Triangle Angle-Sum Theorem
Simplify.
Subtract 142 from each side.
Answer: Therefore, m1 = 63, m2 = 63, and m3 = 38.
Justify The sums of the measures of the angles in each triangle should be m = or 180 m2 + m = or 180
Example 1

17. used to check the reasonableness of the answers found.
Use the Triangle Angle-Sum Theorem
Evaluate By identifying each part of the problem, this complex problem could be separated into three manageable pieces. The properties of triangles were
used to check the reasonableness of the answers found.
Example 1

18. Find the measure of 3.
A. 95
B. 75
C. 57
D. 85
Example 1

19. Concept 3

20. Concept 4

21. GARDENING Find the measure of FLW in the fenced flower garden shown.
Use the Exterior Angle Theorem
GARDENING Find the measure of FLW in the fenced flower garden shown.
mLOW + mOWL = mFLW Exterior Angle Theorem
x + 32 = 2x – 48 Substitution
32 = x – 48 Subtract x from each side.
80 = x Add 48 to each side.
Answer: So, mFLW = 2(80) – 48 or 112.
Example 2

22. The piece of quilt fabric is in the shape of a right triangle
The piece of quilt fabric is in the shape of a right triangle. Find the measure of ACD.
A. 30
B. 40
C. 50
D. 130
Example 2

23. Concept 5

24. Find the measure of each numbered angle.
Find Angle Measures in Right Triangles
Find the measure of each numbered angle.
Exterior Angle Theorem
m1 =
Simplify.
= 70
If 2 s form a linear pair, they are supplementary.
Substitution
70 + m2 = 180
Subtract 70 from each side.
110
Example 3

25. Exterior Angle Theorem
Find Angle Measures in Right Triangles
m = 110
Exterior Angle Theorem
Simplify.
= 46
If 3 s form a linear pair, they are supplementary
m 4 = 180
Simplify.
78+ m4 = 180
Subtract 78 from each side.
102
Example 3

26. Triangle Angle-Sum Theorem m5 + 102+ 41 = 180
Find Angle Measures in Right Triangles
Triangle Angle-Sum Theorem
m = 180
Simplify.
m = 180
Subtract 143 from each side. 37
m1 = 70, m2 = 110, m3 = 46, m4 = 102, m5 =37
Example 3

27. Find m3.
A. 50
B. 45
C. 85
D. 130
Example 3

28. LESSON 4–2
Angles of Triangles