Question

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

Answer 1

Answer:

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°.

Answer 2

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.  $\mathbf{m \angle 1 = 41^{\circ}}$

$\mathbf{m \angle 2 = 85^{\circ}}\\\\\mathbf{m \angle 3 = 95^{\circ}}\\\\\mathbf{m \angle 4 = 85^{\circ}}\\\\\mathbf{m \angle 5 = 36^{\circ}}\\\\\mathbf{m \angle 6 = 49^{\circ}}\\\\\mathbf{m \angle 7 = 106^{\circ}}$

8. x = 12

9. x = 9

10. x = 5

11. x = 7

1. $m \angle 1 = 180 - (76 + 59)$ (sum of angles of any triangle equals 180 degrees)

Solve

$m \angle 1 = 180 - 135\\\\\mathbf{m \angle 1 = 45^{\circ}}$

2. $m \angle 1 = 62 + 67$ (exterior angle of a triangle)

$\mathbf{m \angle 1 = 129^{\circ}}$

3. $m \angle 1 = 152 - 115$ (exterior angle of a triangle)

$\mathbf{m \angle 1 = 37^{\circ}}$

4. $\mathbf{m \angle 2 = m \angle 42 ^{\circ}}$ (vertical angles are congruent)

$m \angle 1 = 180 - (50 + m \angle 2)$ (sum of triangle)

• Substitute

$m \angle 1 = 180 - (50 + 42)\\\\\mathbf{m \angle 1 = 88^{\circ}}$

$m \angle 3 = 180 - (42 + 25)$ (sum of triangle)

• Solve

$m \angle 3 = 180 - 67\\\\\mathbf{m \angle 3 = 113^{\circ}}$

5. $m \angle 1 = 180 - 118$ (angles on a straight line)

$\mathbf{m \angle 1 = 62^{\circ}}$

$m \angle 2 = 180 - (73 + m \angle 1)$ (sum of triangle)

• Substitute

$m \angle 2 = 180 - (73 + 72)\\\\\mathbf{m \angle 2 = 35^{\circ}}$

$118 = 49 + m \angle 2 + m \angle 3$  (exterior angle of a triangle)

• Substitute

$118 = 49 + 35 + m \angle 3\\\\118 = 84 + m \angle 3\\\\118 - 84 = m \angle 3\\\\34 = m \angle 3\\\\\mathbf{m \angle 3 = 34^{\circ}}$

6. $m \angle 1 = 180 - 52$ (supplementary angles)

$\mathbf{m \angle 1 = 128^{\circ}}$

$\mathbf{m \angle 2 = 52^{\circ}}$ (alternate interior angles)

$\mathbf{m \angle 3 = 47^{\circ}}$ (alternate interior angles)

$m \angle 4 = 180 - 47$ (supplementary angles)

$\mathbf{m \angle 4 = 133^{\circ}}$

$m \angle 5 = 180 - (m \angle 2 + m \angle 3)$ (sum of triangle)

Substitute

$m \angle 5 = 180 - (52 + 47)\\\\\mathbf{m \angle 5 = 81^{\circ}}$

7. $\mathbf{m \angle 3 = m \angle 95^{\circ}}$ (vertical angles are congruent)

$m \angle 2 = 180 - m \angle3$ (angles on a straight line)

Substitute

$m \angle 2 = 180 - 95\\\\\mathbf{m \angle 2 = 85^{\circ}}$

$m \angle 4 = m \angle 2$ (vertical angles are congruent)

Substitute

$\mathbf{m \angle 4 = m \angle 85^{\circ}}$

$m \angle 5 = 180 - 144$ (angles on a straight line)

$\mathbf{m \angle 5 = 36^{\circ}}$

$m \angle 6 = 180 - (m \angle 3 + m \angle 5)$ (sum of triangle)

Substitute

$m \angle 6 = 180 - (95 + 36)$

$\mathbf{m \angle 6 = 49^{\circ}}$

$m \angle 7 = 180 - (38 + m \angle 5)$ (sum of triangle)

Substitute

$m \angle 7 = 180 - (38 + 36)$

$\mathbf{m \angle 7 = 106^{\circ}}$

8. $(10x - 11) + (3x - 2) + (3x + 1) = 180^{\circ}$ (sum of triangle)

• Solve for x

$10x - 11 + 3x - 2 + 3x + 1 = 180$

• Add like terms

$10x - 11 + 3x - 2 + 3x + 1 = 180\\16x -12 = 180\\\\16x = 180 + 12\\\\16x = 192\\\\\mathbf{x = 12}$

9.  $(3x - 5) + (7x + 5) + 90 = 180^{\circ}$ (sum of triangle)

• Solve for x

$3x - 5 + 7x + 5 + 90 = 180$

• Add like terms

$10x + 90 = 180\\\\10x = 180 - 90\\\\10x = 90\\\\\mathbf{x = 9}$

10. $(11x - 1) + (20x - 3) = 151$ (exterior angle of a triangle)

• Solve for x

$11x - 1 + 20x - 3 = 151$

• Add like terms

$11x - 1 + 20x - 3 = 151\\31x - 4 = 151\\\\31x = 151 + 4\\\\31x = 155\\\\\mathbf{x = 5}$

11.  $(4x + 13) + (6x + 2) = 14x - 13$ (exterior angle of a triangle)

• Solve for x

$4x + 13 + 6x + 2 = 14x - 13$

• Add like terms

$4x + 13 + 6x + 2 = 14x - 13\\\\10x + 15 = 14x - 13\\\\10x - 14x = -15 - 13\\\\-4x = -28\\\\\mathbf{x = 7}$

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. $\mathbf{m \angle 1 = 128^{\circ}}$

$\mathbf{m \angle 2 = 52^{\circ}}\\\\\mathbf{m \angle 3 = 47^{\circ}}\\\\\mathbf{m \angle 4 = 113^{\circ}}\\\\\mathbf{m \angle 5 = 81^{\circ}}$

7.  $\mathbf{m \angle 1 = 41^{\circ}}$

$\mathbf{m \angle 2 = 85^{\circ}}\\\\\mathbf{m \angle 3 = 95^{\circ}}\\\\\mathbf{m \angle 4 = 85^{\circ}}\\\\\mathbf{m \angle 5 = 36^{\circ}}\\\\\mathbf{m \angle 6 = 49^{\circ}}\\\\\mathbf{m \angle 7 = 106^{\circ}}$

8. x = 12

9. x = 9

10. x = 5

11. x = 7

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