What is the answer to this?

I'm trying to help my cousin for his IGCSE prep, this question struck me. It's been a while since I did O-Level mensuration. Help would be appreciated.

The answer booklet shows x=46.66 and y=133.33 respectively. I would like to know how.

Reply 1

ConfusedPenguin1

Original post

by tigrispanthera

I'm trying to help my cousin for his IGCSE prep, this question struck me. It's been a while since I did O-Level mensuration. Help would be appreciated.
The answer booklet shows x=46.66 and y=133.33 respectively. I would like to know how.

Using the isosceles triangles and labeling some angles as "a" we can show that:

Then using the fact that angles into a triangle sum to 180 we obtain:

This gives a = 23.33, and since x = 2a, x = 46.66

Then since x + y = 180 we get y = 133.33, and we have our answer

(Ps sorry if the pictures are small I can't get them to enlarge for some reason)