Answer:
The answer to your question is below
Step-by-step explanation:
I numbered the squares, see the picture below
Angle 3 and the angle given are vertical angles so they measure the same
angle 3 = 137°
The sum of the angles 1, 2, 3 and 137 equals 360°, so
angle 1 + 137 + angle 3 + 137 = 360
and angle 1 and 3 are vertical angles so angle 1 = angle 3
2angle 1 = 360 - 137 -137
2 angle 1 = 86
angle 1 = 86 /2
angle 1 = 43°
angle 2 = 43°
The angle given and the angle 5 are corresponding angles, they measure the same
angle 5 = 137°
Angle 5 and 6 are vertical angles, they measure the same
angle 6 = 137°
Angle 2 and angle 7 are corresponding angles, they measure the same
angle 7 = 43°
Angle 3 and angle 6 are corresponding angles
angle 6 = 137°
Angle 4 and 7 are vertical angle, so they measure the same
angle 4 = 43°
16731 should be the answer
By using trigonometric relations, we will see that x = 9.97°.
<h3>
How to find the missing angle?</h3>
First, we need to find the bottom cathetus of the smaller triangle, we will use the relation:
Tan(θ) = (opposite cathetus)/(adjacent cathetus).
Where:
- θ = 26°
- Adjacent cathetus = k
- Opposite cathetus = 55ft.
Replacing that we get:
Tan(26°) = 50ft/k
Solving this for k, we get:
k = 55ft/tan(26°) = 112.8 ft
Now, we can see that the longer triangle adds 200ft to this cathetus, so now we will have:
- angle = x
- opposite cathetus = 55ft
- adjacent cathetus = 112.8ft + 200ft = 312.8ft.
Then we have:
Tan(x) = (55ft/312.8ft)
Using the inverse tangent function in both sides, we get:
x = Atan(55ft/312.8ft) = 9.97°
If you want to learn more about right triangles, you can read:
brainly.com/question/2217700
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