Question

Question is the last picture!

Answer 1

The sum of the interior angle of a regular n-sided polygon is (n-2)*180 degrees. For example, a triangle has 3 sides, so the sum is (3-2)*180 degrees = 180 degrees. A square has 4 sides, so the sum is (4-2)*180 degrees = 360 degrees.

From the sum of the interior angles, you can find an individual angle by dividing by the number of sides. A square, for example, has each interior angle = 360 degrees / 4 = 90 degrees.

Look at the diagram. If you know the interior angle, do you know how to find the value of \(x\)?

Answer 2

I just saw your thing ..so it's 8 sides divided by ?

Answer 3

Well, you would use the formulas I just gave you. But let's say for the moment that the interior angle is just \(y\). If you know the value of \(y\), can you find \(x\)?

Answer 4

We've got 8 sides on our figure, so n=8, and the total of all the interior angles is (8-2)*180 = 6*180 = 1080 degrees. We divide that by 8 to find each individual interior angle, so 1080/8 = 135 degrees.

Answer 5

but how does that break down into an answer choice when 135 isn't there? do you have to do more?

Answer 6

Yes, I wanted to make sure you had a chance to catch up — does what we've done so far make sense?

Answer 7

Yes im understanding it!

Answer 8

Great!

So now we have this:



Do you know how to find the value of x?

Answer 9

subtract from 180?

Answer 10

Ding ding ding, we have a winner! :-)

Answer 11

Thank you so much! Can you help me with another one?

Answer 12

You explained that really well

Answer 13

Ask away :-)

Answer 14

Yikes! :-)

Answer 15

Here's how I would approach that. First, find the unknown angle at the right end of the triangle on the left.

Answer 16

okay i have a diffrent one..

Answer 17

Having found that angle, do you know what the angle on the other side made by the same two lines would be? If so, then use the first formula I gave you to find out the sum of the interior angles of the 5-sided thing on the right, then subtract out all the angles that aren't x, and what is left is x.

Answer 18

Do you add 180 or 360? I have no idea how to do this one..

Answer 19

is the angle on the other side 180 or the diffrence of 180?

Answer 20

Okay, what if you have two lines crossing so that they make right angles?

Answer 21

a and a would be identical, right? Wouldn't that also mean that the unlabeled angles were identical?

Answer 22

yes because they are congruent making them the same?

Answer 23

Now let's pretend we can twist one of the lines so that it squashes the a angles (and the unlabeled angles get bigger). Both of the a's will remain equal to each other, right? And the unlabeled angles will also be equal to each other.

Answer 24

yes and.....

Answer 25

And each pair of a + (unlabeled) will always add up to 180, so the whole thing adds up to 360.

Answer 26

But the important thing as far as this problem is concerned is that the opposite angles are always congruent. So, having found the missing angle in the triangle on the left, we know the corresponding angle on the right.

Answer 27

so...the "unlabeled" is 240? there has to be more steps...

Answer 28

No, not 240. What did you find for the missing value in the triangle?

Answer 29

I see 50.1 and 53.1 as the known angles in the triangle. 50.1 + 53.1 + ? = 180.

Answer 30

well i did 360-120 =240 im not really sure..

Answer 31

Sum of the angles in the triangle is 180 degrees, always: n = 3, (n-2)*180 = (3-2)*180 = 180 degrees.

Answer 32

so the ? = 103.2

Answer 33

We know that two of the angles are 50.1 and 53.1 degrees, so how large does the remaining angle have to be to get us to 180?

\[50.1 + 53.1 + y = 180\]
subtract 50.1 and 53.1 from both sides
\[50.1 + 53.1 - 50.1 - 53.1 + y = 180 - 50.1 -53.1\]
\[y = 180 - 50.1 - 53.1 = 76.8\]

Answer 34

then what do you do?

Answer 35

Okay, so that means that the angle on the left end of the 5-sided polygon (the one opposite x) is also 76.8 degrees, because angles made by two lines crossing are always congruent across the intersection point.

Answer 36

76.8 is the angle and x is 98.3?

Answer 37

That's what I got!

Answer 38

What was the answer to this one?

Answer 39

&& thank you so much for helping me!

Answer 40

Your other question has us work backwards with the angle formulas.

The sum of all the angles in an n-sided polygon is \((n-2)*180\), and each individual angle would then be \[\frac{(n-2)*180}{n}\]

We know that the angle in our mystery polygon is 120, so we just need to solve
\[120 = \frac{(n-2)*180}{n}\]

Answer 41

is n 120?

Answer 42

That will give us the number of sides, and we can find the total by multiplying the number of sides (same as the number of angles) by 120.

Answer 43

didnt we already do this one or we never finished it? haha

Answer 44

\[120 = \frac{(n-2)*180}{n}\]Multiply both sides by \(n\):
\[120n = \frac{n(n-2)*180}{n} = 180(n-2) = 180n-360\]\[120n=180n-360\]
Add 360 to both sides and subtract 120n from both sides to get:
\[360 = 60n\]\[n = 6\]

So our mystery polygon has 6 sides, 6 angles at 120 degrees each. What is the answer for the total of the angles?

Answer 45

(we never finished it)

Answer 46

12?

Answer 47

Wait no it's 720 because you multiply 6 by 120

Answer 48

There you go!

Answer 49

Can you help me with translations & reflections?

Answer 50

Let's find out :-)

Answer 51

Okay, let's look at at the first one. Do you have any idea about how to do it?

Answer 52

h is 1,3

Answer 53

Yes, the untranslated H is at (1,3). But it will be somewhere else after we translate it the same way we did the triangle.

If you had to describe how any point on the first triangle was moved to get to the same spot on the second triangle, how would you do it?

Answer 54

For example, what happens to C to make it into C'?

Answer 55

6 units up, 3 to the left

Answer 56

Correct! So if we do that same thing to H, where does H' end up?

Answer 57

-3,-3?

Answer 58

i think its 7,6

Answer 59

Mmm, no :-)

Our translation of "6 units up, 3 to the left" is the same as adding 3 to the x coordinate, and 6 to the y coordinate, yes? Actually, it's "6 units up, 3 to the right", I didn't notice you had that part backwards...

Answer 60

So yes, (7,6) is correct (our messages crossed paths)