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worty [1.4K]
2 years ago
5

Solve for x: x = Answers: 22.5 30 45

Mathematics
1 answer:
AVprozaik [17]2 years ago
6 0
Answer: 22.5 degrees

Step-by-Step Explanation:

As we can see, we are given a line, which is a straight angle. Hence, it will be of 180 degrees.

=> All the angles sum up to 180.

Therefore,
=> 3x + x + 90 = 180
= 4x + 90 = 180
= 4x = 180 - 90 = 90
=> x = 90/4 = 22.5

Therefore, x = 22.5 degrees

Verification:

=> 3x + x + 90 = 180
= 3(22.5) + 22.5 + 90 = 180
= 67.5 + 22.5 + 90 = 180
= 90 + 90 = 180
=> 180 = 180
=> LHS = RHS
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Answer:

93.39

Step-by-step explanation:

So the sum of exterior angles of the convex octagon is: 360 degrees

This means if we add all the equations that represent each angle, we can set it equal to 360 and solve for x

(x+14) + (2x-3) + (3x+8) + (3x+16) + (2x-17) + (3x-4) + (3x-12) + (6x)

Group like terms

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Add like terms

23x+2

Now let's set the sum of exterior angles to 360

23x+2 = 360

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x\approx 15.565

So by looking at all these, it appears that 6x is the highest value, given that x is positive. The way I estimated, is approximately 15.5, whenever I saw an equation like x+14, I estimated it's about 2x, since 14 is not exactly, but close to 15.5. I did this with each polynomial given. You could also manually check each one

Original equation

6x

Subsitute

6(15.565)

Simplify

93.39

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