Gina Wilson All Things Algebra Unit 4: Congruent Triangles
(Angles of Triangles) Help!!

By applying the knowledge of the sum of triangle, angles on a straight line and angles formed when two parallel lines are intersected, we have the following values of x and missing angles:

1. m<1 = 45

2. m<1 = 129

3. m<1 = 37

4. m<1 = 88

m<2 = 42

m<3 = 113

5. m<1 = 62

m<2 = 35

m<3 = 34

6. m<1 = 128

m<2 = 52

m<3 = 47

m<4 = 113

m<5 = 81

7.  

8. x = 12

9. x = 9

10. x = 5

11. x = 7

1. (sum of angles of any triangle equals 180 degrees)

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2. (exterior angle of a triangle)

3. (exterior angle of a triangle)

4. (vertical angles are congruent)

(sum of triangle)

(sum of triangle)

5. (angles on a straight line)

(sum of triangle)

 (exterior angle of a triangle)

6. (supplementary angles)

(alternate interior angles)

(alternate interior angles)

(supplementary angles)

(sum of triangle)

Substitute

7. (vertical angles are congruent)

(angles on a straight line)

Substitute

(vertical angles are congruent)

Substitute

(angles on a straight line)

(sum of triangle)

Substitute

(sum of triangle)

Substitute

8. (sum of triangle)

9.   (sum of triangle)

10. (exterior angle of a triangle)

11.   (exterior angle of a triangle)

In summary, by applying the knowledge of the sum of triangle, angles on a straight line and angles formed when two parallel lines are intersected, we have the following values of x and missing angles:

1. m<1 = 45

2. m<1 = 129

3. m<1 = 37

4. m<1 = 88

m<2 = 42

m<3 = 113

5. m<1 = 62

m<2 = 35

m<3 = 34

6.

7.  

8. x = 12

9. x = 9

10. x = 5

11. x = 7

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1. m∠1 = 48°

2. m∠1 = 129°

3. m∠1 = 37°

4. m∠1 = 88°

m∠2 = 42°

m∠3 = 113°

5. m∠1 = 72°

m∠2 = 35°

m∠3 = 24°

6. m∠1 = 128°

m∠2 = 52°

m∠3 = 47°

m∠4 = 133°

m∠5 = 81°

7. m∠1 = 41°

m∠2 = 85°

m∠3 = 95°

m∠4 = 85°

m∠5 = 36°

m∠6 = 49°

m∠7 = 106°

8. x = 12°

9. x = 9°

10. x = 5°

11. x = 7°.  

Step-by-step explanation:

1. 76° + 56° + m∠1 = 180°

∴ m∠1 = 180° - (76° + 56°) = 48°

m∠1 = 48°

2. m∠1 = 67° + 62° = 129°

m∠1 = 129°

3. m∠1 = 152° - 115° = 37°

m∠1 = 37°

4. m∠1 = 180° - (52° + 42°) = 88°

m∠1 = 88°

m∠2 = 42°

m∠3 = 180 - (42° + 25°) = 113°

m∠3 = 113°

5. m∠1 = 180° - 118° = 72°

m∠1 = 72°

m∠2 = 180° - 72° - 73° = 35°

m∠2 = 35°

m∠3 = 73° - 49° = 24°

m∠3 = 24°

6. m∠5 = 180° - m∠52° - m∠47° = 81°

m∠5 = 81°

m∠1 = 81° + 47° = 128°

m∠1 = 128°

m∠2 = 52°

m∠3 = 47°

m∠4 = 180° - 47° = 133°

m∠4 = 133°

7. m∠3 = 95°

m∠5 = 180° - 144° = 36°

m∠5 = 36°

m∠6 = 180° - 95° - 36° = 49°

m∠6 = 49°

m∠4 = 180° - 95° = 85°

m∠4 = 85°

m∠2 = 85°

m∠7 = 360° - (38° + 85° + (180° - 49°)) = 106°

m∠7 = 106°

m∠1 = 360° - (85° + 90° + 144°) = 41°

m∠1 = 41°

8. (10·x - 11)° + (3·x - 2)° + (3·x + 1)° = 16·x° - 12° = 180°

16·x = 180°+ 12° = 192°

x° = 192°/16 = 12°

x = 12°

9. (3·x - 5)° + (7·x + 5)° + 90 = 180°

10·x + 90° = 180°

10·x  = 180°- 90° = 90°

10·x = 90°

x = 90°/10 = 9°

x = 9°

10. 180 - 151 = 29°

(11·x - 1)° + (20·x - 3)° + 29° = 180°

31·x° + 25° = 180°

31·x°  = 180° - 25° = 155°

31·x°  = 155°

x = 155/31 = 5°

x = 5°

12. (4·x + 13) + (6·x + 2) + 180 - (14·x - 13)

208° - 4·x° = 180°

208° -  180° = 4·x°

28° = 4·x°

4·x° = 28°

x = 28°/4 = 7°

x = 7°.

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step-by-step explanation: