Please help - geometry homework question!

[passthestraws]

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?! 🙈

[SeptemberDays]

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]

Bit, not but.

[Hecateh]

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

[passthestraws]

@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.

[passthestraws]

@Hecateh thanks for making me feel better 😂

[TeaStory]

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]

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]

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

Not GCSE, year 7 homework!

[justchecking1]

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]

PRQ is 36 I mean

[passthestraws]

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

[SeptemberDays]

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]

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

[Damia]

Does it say PR is equal to RU or anything?

[passthestraws]

@Damia no, it gives no other information like that

[Cloverisover]

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]

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]

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 it’s a pentagon. So SRU is (120+36)-108

Does that make sense?

[justchecking1]

@passthestraws

[passthestraws]

@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?

[passthestraws]

Not form, but "are part of"!

[SeptemberDays]

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]

Fab, thank you!!