Mathematics, 23.10.2020 03:01 kenzie5889

2-3 Additional Practice Parallel Lines and Triangle Angle Sums
For Exercises 1-6, find the value of each variable.

2-3 Additional Practice

Parallel Lines and Triangle Angle Sums
For Exercises 1-6, find the value

Answers: 1

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Answer from: tinyturtles

The angles in a triangle add up to 180 degrees

The value of x is 25The value of x is 73The value of x is 60The values of x, y and z are 67, 113 and 180The values of x, y and z are 56, 81 and 99The values of x, y and z are 54, 114 and 6

Exercise 1

We have:

$\mathbf{x + 92 + 63 = 180}$ --- sum of angles is 180

$\mathbf{x + 155 = 180}$

Subtract 155 from both sides

$\mathbf{x = 25}$

Hence, the value of x is 25

Exercise 2

We have:

$\mathbf{x + 20 + 87 = 180}$ --- sum of angles is 180

$\mathbf{x + 107 = 180}$

Subtract 107 from both sides

$\mathbf{x = 73}$

Hence, the value of x is 73

Exercise 3

We have:

$\mathbf{x + 80 + 40 = 180}$ --- sum of angles is 180

$\mathbf{x + 120 = 180}$

Subtract 120 from both sides

$\mathbf{x = 60}$

Hence, the value of x is 60

Exercise 4

First, we calculate the value of x using:

$\mathbf{x + 85 + 28 = 180}$ --- sum of angles is 180

$\mathbf{x + 113 = 180}$

Subtract 113 from both sides

$\mathbf{x = 67}$

x and y are on a straight line.

So, we have:

$\mathbf{y = 180 - x}$ --- supplementary angles

$\mathbf{y = 180 - 67}$

$\mathbf{y = 113}$

Calculate the value of z using:

$\mathbf{z + y + 15 = 180}$ --- sum of angles is 180

$\mathbf{z + 113 + 15 = 180}$

$\mathbf{z + 128 = 180}$

Subtract 128 from both sides

$\mathbf{z = 52}$

Hence, the values of x, y and z are 67, 113 and 180

Exercise 5

First, we calculate the value of z using:

$\mathbf{z + 57 + 24 = 180}$ --- sum of angles is 180

$\mathbf{x + 81 = 180}$

Subtract 81 from both sides

$\mathbf{z = 99}$

z and y are on a straight line.

So, we have:

$\mathbf{y = 180 - z}$ --- supplementary angles

$\mathbf{y = 180 - 99}$

$\mathbf{y = 81}$

Calculate the value of x using:

$\mathbf{x + y + 43 = 180}$ --- sum of angles is 180

$\mathbf{x + 81 + 43 = 180}$

$\mathbf{x + 124 = 180}$

Subtract 128 from both sides

$\mathbf{x = 56}$

Hence, the values of x, y and z are 56, 81 and 99

Exercise 6

First, we calculate the value of z using:

$\mathbf{z + 84 + 30 = 180}$ --- sum of angles is 180

$\mathbf{x + 114 = 180}$

Subtract 114 from both sides

$\mathbf{z = 66}$

z and y are on a straight line.

So, we have:

$\mathbf{y = 180 - z}$ --- supplementary angles

$\mathbf{y = 180 - 66}$

$\mathbf{y = 114}$

Calculate the value of x using:

$\mathbf{x + y + 12 = 180}$ --- sum of angles is 180

$\mathbf{x + 114 + 12 = 180}$

$\mathbf{x + 126 = 180}$

Subtract 126 from both sides

$\mathbf{x = 54}$

Hence, the values of x, y and z are 54, 114 and 6

Read more about angles in a triangle at:

link

Answer from: Browardlovesangel

Answer/Step-by-step explanation:

1. 180° - (92° + 63°) = x (sum of angles in a ∆)

180° - 155° = x

25° = x

x = 25°

2. 180° - (20° + 87°) = x (sum of interior angles in a ∆)

180° - 107° = x

73° = x

x = 73°

3. 180° - (80° + 40°) = x (sum of interior angles in a ∆)

180° - 120° = x

60° = x

x = 60°

4. 180° - (28° + 85°) = x (sum of interior angles in a ∆)

180° - 113° = x

67° = x

x = 67°

180° - 67° = y (angle in a straight line)

113° = y

y = 113°

180° - (113° + 15°) = x (sum of interior angles in a ∆)

180° - 128° = z

73° = z

z = 52°

5. 180° - (24° + 57°) = z (sum of interior angles in a ∆)

180° - 81° = z

99° = z

z = 99°

180° - 99° = y (angle in a straight line)

81° = y

y = 81°

180° - (81° + 43°) = x (sum of interior angles in a ∆)

180° - 124° = x

56° = x

x = 56°

6. The figure for question is not fully displayed. Follow the same steps used in solving from question 1 to 5.

Answer from: Quest

to find the perimeter of the rectangle this is the expression:

x-9+x-9+3x-4+3x-4=138

if we simplify it:

8x-26=138

remember, 138 is what it all adds up to

the length is 11.5cm

the width is 57.5cm

the area is 661.25cm^2

the answers might not be correct use at own risk

Answer from: Quest

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Part 2 of this question read the rest of the information

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2-3 Additional Practice Parallel Lines and Triangle Angle Sums
For Exercises 1-6, find the va...