1. 7-3 Angles in Triangles Warm Up Problem of the Day Lesson Presentation
Course 3

2. 7-3 Angles in Triangles Warm Up Solve each equation.
Course 3
7-3
Angles in Triangles
Warm Up
Solve each equation.
x + 37 = 180
2. x = 180
3. 2x + 18 = 180
= 2x x
x = 81
x = 79
x = 81
x = 36

3. 7-3 Angles in Triangles Problem of the Day
Course 3
7-3
Angles in Triangles
Problem of the Day
What is the one hundred fiftieth day of a non-leap year?
May 30

4. 7-3 Angles in Triangles Learn to find unknown angles in triangles.
Course 3
7-3
Angles in Triangles
Learn to find unknown angles in triangles.

5. Insert Lesson Title Here
Course 3
7-3
Angles in Triangles
Insert Lesson Title Here
Vocabulary
Triangle Sum Theorem
acute triangle
right triangle
obtuse triangle
equilateral triangle
isosceles triangle
scalene triangle

6. Course 3
7-3
Angles in Triangles
If you tear off two corners of a triangle and place them next to the third corner, the three angles seem to form a straight line.

7. Course 3
7-3
Angles in Triangles
Draw a triangle and extend one side. Then draw a line parallel to the extended side, as shown.
The sides of the triangle are transversals to the parallel lines.
The three angles in the triangle can be arranged to form a straight line or 180°.

8. Course 3
7-3
Angles in Triangles
An acute triangle has 3 acute angles. A right triangle has 1 right angle. An obtuse triangle has 1 obtuse angle.

9. Course 3
7-3
Angles in Triangles
Additional Example 1A: Finding Angles in Acute, Right and Obtuse Triangles
Find p° in the acute triangle.
73° + 44° + p° = 180°
117° + p° = 180°
–117° –117°
p° = 63°

10. Course 3
7-3
Angles in Triangles
Additional Example 1B: Finding Angles in Acute, Right, and Obtuse Triangles
Find c° in the right triangle.
42° + 90° + c° = 180°
132° + c° = 180°
–132° –132°
c° = 48°

11. Course 3
7-3
Angles in Triangles
Additional Example 1C: Finding Angles in Acute, Right, and Obtuse Triangles
Find m° in the obtuse triangle.
23° + 62° + m° = 180°
85° + m° = 180°
–85° –85°
m° = 95°

12. 7-3 Angles in Triangles Check It Out: Example 1A
Course 3
7-3
Angles in Triangles
Check It Out: Example 1A
Find a° in the acute triangle.
88° + 38° + a° = 180°
38°
126° + a° = 180°
–126° –126°
a° = 54° a°
88°

13. 7-3 Angles in Triangles Check It Out: Example 1B
Course 3
7-3
Angles in Triangles
Check It Out: Example 1B
Find b in the right triangle.
38°
38° + 90° + b° = 180°
128° + b° = 180°
–128° –128°
b° = 52° b°

14. 7-3 Angles in Triangles Check It Out: Example 1C
Course 3
7-3
Angles in Triangles
Check It Out: Example 1C
Find c° in the obtuse triangle.
24° + 38° + c° = 180°
38°
62° + c° = 180°
24° c°
–62° –62°
c° = 118°

15. Course 3
7-3
Angles in Triangles
An equilateral triangle has 3 congruent sides and 3 congruent angles. An isosceles triangle has at least 2 congruent sides and 2 congruent angles. A scalene triangle has no congruent sides and no congruent angles.

16. Course 3
7-3
Angles in Triangles
Additional Example 2A: Finding Angles in Equilateral, Isosceles, and Scalene Triangles
Find the angle measures in the equilateral triangle.
3b° = 180°
Triangle Sum Theorem
3b° ° =
Divide both sides by 3.
b° = 60°
All three angles measure 60°.

17. Course 3
7-3
Angles in Triangles
Additional Example 2B: Finding Angles in Equilateral, Isosceles, and Scalene Triangles
Find the angle measures in the isosceles triangle.
62° + t° + t° = 180°
Triangle Sum Theorem
62° + 2t° = 180°
Combine like terms.
–62° –62°
Subtract 62° from both sides.
2t° = 118°
2t° = 118°
Divide both sides by 2.
t° = 59°
The angles labeled t° measure 59°.

18. Course 3
7-3
Angles in Triangles
Additional Example 2C: Finding Angles in Equilateral, Isosceles, and Scalene Triangles
Find the angle measures in the scalene triangle.
2x° + 3x° + 5x° = 180°
Triangle Sum Theorem
10x° = 180°
Combine like terms.
Divide both sides by 10.
x = 18°
The angle labeled 2x° measures 2(18°) = 36°, the angle labeled 3x° measures 3(18°) = 54°, and the angle labeled 5x° measures 5(18°) = 90°.

19. 7-3 Angles in Triangles Check It Out: Example 2A
Course 3
7-3
Angles in Triangles
Check It Out: Example 2A
Find the angle measures in the isosceles triangle.
39° + t° + t° = 180°
Triangle Sum Theorem
39° + 2t° = 180°
Combine like terms.
–39° –39°
Subtract 39° from both sides.
2t° = 141°
2t° = 141°
Divide both sides by 2
39°
t° = 70.5° t°
The angles labeled t° measure 70.5°. t°

20. 7-3 Angles in Triangles Check It Out: Example 2B
Course 3
7-3
Angles in Triangles
Check It Out: Example 2B
Find the angle measures in the scalene triangle.
3x° + 7x° + 10x° = 180°
Triangle Sum Theorem
20x° = 180°
Combine like terms.
Divide both sides by 20.
x = 9°
10x°
The angle labeled 3x° measures 3(9°) = 27°, the angle labeled 7x° measures 7(9°) = 63°, and the angle labeled 10x° measures 10(9°) = 90°.
3x°
7x°

21. 7-3 Angles in Triangles Check It Out: Example 2C
Course 3
7-3
Angles in Triangles
Check It Out: Example 2C
Find the angle measures in the equilateral triangle.
3x° = 180°
Triangle Sum Theorem
3x° ° = x°
x° = 60° x° x°
All three angles measure 60°.

22. Course 3
7-3
Angles in Triangles
Additional Example 3: Finding Angles in a Triangle that Meets Given Conditions
The second angle in a triangle is six times as large as the first. The third angle is half as large as the second. Find the angle measures and draw a possible picture.
Let x° = the first angle measure. Then 6x° = second angle measure, and (6x°) = 3x° = third angle measure. 12

23. Additional Example 3 Continued
Course 3
7-3
Angles in Triangles
Additional Example 3 Continued
Let x° = the first angle measure. Then 6x° = second angle measure, and (6x°) = 3x° = third angle. 12
x° + 6x° + 3x° = 180°
Triangle Sum Theorem
10x° = 180°
Combine like terms.
Divide both sides by 10.
x° = 18°

24. Additional Example 3 Continued
Course 3
7-3
Angles in Triangles
Additional Example 3 Continued
Let x° = the first angle measure. Then 6x° = second angle measure, and (6x°) = 3x° = third angle. 12
x° = 18°
The angles measure 18°, 54°, and 108°. The triangle is an obtuse scalene triangle.
3 • 18° = 54°
6 • 18° = 108°
X° = 18°

25. 7-3 Angles in Triangles Check It Out: Example 3
Course 3
7-3
Angles in Triangles
Check It Out: Example 3
The second angle in a triangle is three times larger than the first. The third angle is one third as large as the second. Find the angle measures and draw a possible picture.
Let x° = the first angle measure. Then 3x° = second angle measure, and (3x°) = x° = third angle measures. 13

26. Check It Out: Example 3 Continued
Course 3
7-3
Angles in Triangles
Check It Out: Example 3 Continued
Let x° = the first angle measure. Then 3x° = second angle measure, and (3x°) = 3x° = third angle. 13
x° + 3x° + x° = 180°
Triangle Sum Theorem
5x° = 180°
Combine like terms.
Divide both sides by 5.
x° = 36°

27. Check It Out: Example 3 Continued
Course 3
7-3
Angles in Triangles
Check It Out: Example 3 Continued
Let x° = the first angle measure. Then 3x° = second angle measure, and (3x°) = x° = third angle. 13
The angles measure 36°, 36°, and 108°. The triangle is an obtuse isosceles triangle.
x° = 36°
3 • 36° = 108°
x° = 36°
36°
108°

28. 7-3 Angles in Triangles Lesson Quiz: Part I
Course 3
7-3
Angles in Triangles
Lesson Quiz: Part I
1. Find the missing angle measure in the acute triangle shown.
38°
2. Find the missing angle measure in the right triangle shown.
55°

29. 7-3 Angles in Triangles Lesson Quiz: Part II
Course 3
7-3
Angles in Triangles
Lesson Quiz: Part II
3. Find the missing angle measure in an acute triangle with angle measures of 67° and 63°.
50°
4. Find the missing angle measure in an obtuse triangle with angle measures of 10° and 15°.
155°