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23 replies

passthestraws · 25/06/2019 16:43

Question 1 - A regular pentagon and a regular hexagon overlap. What is the value of x?

Question 2 - a regular pentagon is shown together with three sides. What is the size of angle SRU?

Completely beyond me - can any of you please help me not to look so stupid to my DS?! ðŸ™ˆ

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SeptemberDays · 25/06/2019 16:52

The but in the hexagon but not the Pentagon will be (180-108)/2 because the top is horizontal and the top lines of the Pentagon are equal angles from that.

So x is 120-((180-108)/2).

I don't know what you mean by sru?

SeptemberDays · 25/06/2019 16:53

Bit, not but.

Hecateh · 25/06/2019 16:54

Wow? Sorry, can't help with that one. I thought I'd let you know - you are not alone,

passthestraws · 25/06/2019 16:56

@SeptemberDays thank you!

SRU - photo 2, the shaded bit. I have assumed they mean the angle between the points S R and U which I've shaded in pencil.

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passthestraws · 25/06/2019 16:56

@Hecateh thanks for making me feel better ðŸ˜‚

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TeaStory · 25/06/2019 17:05

For the first one, the overlapped area is a five-sided polygon. The interior angles of a five-sided polygon add up to 540 degrees.

The interior angle of a regular pentagon is 108 degrees, the interior angle of a regular hexagon is 120 degrees. Look at the overlap shape - it has two of the hexagon corners and two of the pentagon corners, plus x.

So x = 540 - (120 + 120 + 108 + 108)

x = 540 - 456

x = 84 degrees.

SeptemberDays · 25/06/2019 17:11

Oops, didn't spot second photo.

Assuming grey line is part of a hexagon again
PRQ is (180-108)/2 Internal angles of a triangle
S RP is 108-PQR
PRU is 120-SRP

Gcse? The second question is easier than the first and I'd start with that if you're explaining it.

passthestraws · 25/06/2019 17:35

Thank you, although I still don't understand the second one!

Not GCSE, year 7 homework!

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justchecking1 · 25/06/2019 17:52

SRU is 48 by my working. You can work out the angle of the small triangle at the bottom (36)
Then SRU =(120 +36)-108
=48

justchecking1 · 25/06/2019 17:53

PRQ is 36 I mean

passthestraws · 25/06/2019 20:30

@justchecking1 thanks - which small triangle did you work out and how?! ðŸ˜© so confused!!

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SeptemberDays · 25/06/2019 23:41

The triangle with the points PRQ has one ang!e of 108 (Pentagon corner) the other two angles are equal and all three add to 180 (angles in a triangle) so (180-108)/2 is 36

passthestraws · 26/06/2019 06:49

PRQ is 36, understood. So where does 120 come from?! Am I being really stupid?

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Damia · 26/06/2019 07:25

Does it say PR is equal to RU or anything?

passthestraws · 26/06/2019 08:39

@Damia no, it gives no other information like that

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Cloverisover · 26/06/2019 09:49

Are the other 3 lines assumed to be half a hexagon then? I've not done this kind of maths for 30 years, have forgotten everything and am dying to know the answer!

Damia · 26/06/2019 10:17

The only other thing I can remember is that if you have a regular shape all exterior angles will add up to 360 if you draw straight lines from the sides and continue out, so 72 each e.g. going from QR line and extending straight to some new point y the total SRy angle would be 72, and from PQ out is the same, or the opposite direction from QP. I'm sure it must use that in some way

justchecking1 · 26/06/2019 11:15

PRU is 120 because this is a hexagon (or half a hexagon) and they have internal angles of 120.

PRQ is 36 (as worked out above)

QRU is therefore 120 + 36. We know that QRS is 108 because itâ€™s a pentagon. So SRU is (120+36)-108

Does that make sense?

justchecking1 · 26/06/2019 11:16

@passthestraws

passthestraws · 26/06/2019 13:02

@justchecking1 aha I think I've finally got it, thanks for explaining! So we have to assume that the lines coming off the pentagon form a regular hexagon?

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passthestraws · 26/06/2019 13:03

Not form, but "are part of"!

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SeptemberDays · 26/06/2019 13:13

Yes assume sides of a hexagon. Because if they're not there is no way to calculate it. Also because I think we all assumed the two questions were related. Admittedly, it is poorly worded and should have been explicit.

passthestraws · 26/06/2019 13:15

Fab, thank you!!

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