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.
The angles in a triangle add up to 180 degrees
Exercise 1
We have:
[tex]\mathbf{x + 92 + 63 = 180}[/tex] --- sum of angles is 180
[tex]\mathbf{x + 155 = 180}[/tex]
Subtract 155 from both sides
[tex]\mathbf{x = 25}[/tex]
Hence, the value of x is 25
Exercise 2
We have:
[tex]\mathbf{x + 20 + 87 = 180}[/tex] --- sum of angles is 180
[tex]\mathbf{x + 107 = 180}[/tex]
Subtract 107 from both sides
[tex]\mathbf{x = 73}[/tex]
Hence, the value of x is 73
Exercise 3
We have:
[tex]\mathbf{x + 80 + 40 = 180}[/tex] --- sum of angles is 180
[tex]\mathbf{x + 120 = 180}[/tex]
Subtract 120 from both sides
[tex]\mathbf{x = 60}[/tex]
Hence, the value of x is 60
Exercise 4
First, we calculate the value of x using:
[tex]\mathbf{x + 85 + 28 = 180}[/tex] --- sum of angles is 180
[tex]\mathbf{x + 113 = 180}[/tex]
Subtract 113 from both sides
[tex]\mathbf{x = 67}[/tex]
x and y are on a straight line.
So, we have:
[tex]\mathbf{y = 180 - x}[/tex] --- supplementary angles
[tex]\mathbf{y = 180 - 67}[/tex]
[tex]\mathbf{y = 113}[/tex]
Calculate the value of z using:
[tex]\mathbf{z + y + 15 = 180}[/tex] --- sum of angles is 180
[tex]\mathbf{z + 113 + 15 = 180}[/tex]
[tex]\mathbf{z + 128 = 180}[/tex]
Subtract 128 from both sides
[tex]\mathbf{z = 52}[/tex]
Hence, the values of x, y and z are 67, 113 and 180
Exercise 5
First, we calculate the value of z using:
[tex]\mathbf{z + 57 + 24 = 180}[/tex] --- sum of angles is 180
[tex]\mathbf{x + 81 = 180}[/tex]
Subtract 81 from both sides
[tex]\mathbf{z = 99}[/tex]
z and y are on a straight line.
So, we have:
[tex]\mathbf{y = 180 - z}[/tex] --- supplementary angles
[tex]\mathbf{y = 180 - 99}[/tex]
[tex]\mathbf{y = 81}[/tex]
Calculate the value of x using:
[tex]\mathbf{x + y + 43 = 180}[/tex] --- sum of angles is 180
[tex]\mathbf{x + 81 + 43 = 180}[/tex]
[tex]\mathbf{x + 124 = 180}[/tex]
Subtract 128 from both sides
[tex]\mathbf{x = 56}[/tex]
Hence, the values of x, y and z are 56, 81 and 99
Exercise 6
First, we calculate the value of z using:
[tex]\mathbf{z + 84 + 30 = 180}[/tex] --- sum of angles is 180
[tex]\mathbf{x + 114 = 180}[/tex]
Subtract 114 from both sides
[tex]\mathbf{z = 66}[/tex]
z and y are on a straight line.
So, we have:
[tex]\mathbf{y = 180 - z}[/tex] --- supplementary angles
[tex]\mathbf{y = 180 - 66}[/tex]
[tex]\mathbf{y = 114}[/tex]
Calculate the value of x using:
[tex]\mathbf{x + y + 12 = 180}[/tex] --- sum of angles is 180
[tex]\mathbf{x + 114 + 12 = 180}[/tex]
[tex]\mathbf{x + 126 = 180}[/tex]
Subtract 126 from both sides
[tex]\mathbf{x = 54}[/tex]
Hence, the values of x, y and z are 54, 114 and 6
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