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21. In n ABC, m∠ A 5 m∠ B 1 308 and m∠ C 5 m∠ B 1 608. Find the measure of each angle.
22. In n ABC, m∠ A 5 2(m∠ B) and m∠ C 5 3(m∠ B). Find the measure of each angle.
Find the values of x and y.
23.
308
x 8
y 8
24.
398568
508x 8
y 8
25. 708
788748
x 8
y 8
26. Metal Brace The diagram shows the dimensions of a metal brace used for strengthening a vertical and horizontal wooden junction. Classify the triangle formed by its sides. Then copy the triangle, measure the angles, and classify the triangle by its angles.
7.14 in.10.5 in.
7.7 in.
Practice B continuedFor use with the lesson “Apply Triangle Sum Properties”
Lesson Apply Triangle Sum PropertiesTeaching Guide
1. Check drawings. 2. Check drawings. It is impossible to construct triangles with 3 congruent sides and 1 right angle and with 3 congruent sides and 1 obtuse angle.
Technology Activity
1. The angle measures change; the sum of the angle measures stays the same.
2. Sample answer: 5 triangles; the sum of the angle measures is 1808. 3. The sum of the measures of the angles of any triangle is 1808.
Practice Level A
1. equilateral 2. isosceles 3. scalene
4. isosceles 5. right 6. acute 7. obtuse
8. equiangular 9. 55 10. 35 11. 45 12. 158
13. 90 14. 62 15. m∠ 1 5 608
16. m∠ 1 5 608; m∠ 2 5 308; m∠ 3 5 808
17. m∠ 1 5 708; m∠ 2 5 658; m∠ 3 5 958
18. m∠ A 5 458; m∠ B 5 908; m∠ C 5 458
19. scalene; obtuse
Practice Level B
1. sometimes 2. never 3. never 4. sometimes
5. scalene, obtuse 6. scalene, right
7. isosceles, acute
8.
x
y
2
2
A C
B
9.
B x
y
2
2
C
A
scalene; right triangle scalene; not a right triangle
10.
x
y
2
2
B
C
A
isosceles; not a right triangle
11. 30; right 12. 25; acute 13. 120; acute
14. 1318 15. 1008 16. 1258 17. 368 18. 1228
19. 1228 20. 388 21. m∠ A 5 608, m∠ B 5 308, m∠ C 5 908 22. m∠ A 5 608, m∠ B 5 308, m∠ C 5 908
23. 60, 30 24. 45, 51 25. 24, 66
26. scalene; right
Practice Level C
1. scalene; 20; acute 2. isosceles; 25; acute
3. equilateral; 60; equiangular 4. x 5 10; y 5 71
5. x 5 50; y 5 33 6. x 5 15; y 5 42
7. x 5 85; y 5 58 8. 608 9. 1208 10. 608
11. 1208 12. 308 13. 308 14. 748
15. m∠ B 5 1158; m∠ C 5 238 16. 8 in. by 11 in. by 11 in.; 8 in. by 8 in. by 14 in.
TS , and the base is } RT ; m∠ 1 5 55°, m∠ 2 5 110°
2. The legs are }
RS and }
TS , and the hypotenuse is } RT ; m∠ SRT 5 54°, m∠ 1 5 144°
Challenge Practice
1. (5, 9) 2. (9, 1)
x
y
A(3, 3)
B(7, 5)
C (5, 9)
x
y
A(3, 3)
D(9, 1)
B(7, 5)
3. 608, 608, 608 4. 638, 368, 818; acute
5. x 5 29, y 5 64 6. x 5 12.9, y 5 51.3
7. m∠ A 5 m∠ 1 8. GIVEN: n ABC PROVE: Sum of exterior angles of n ABC
is 3608.By the definition of a straight angle, you know that m∠ 1 1 m∠ 2 5 1808, m∠ 3 1 m∠ 4 5 1808, and m∠ 5 1 m∠ 6 5 1808. So, it follows that the sum of all six angles is 1808 1 1808 1 1808 5 5408.