Angles
1a) Find angle x and y in the following diagram?
b) Next, Find Angle b in the diagram below
Here is the backwards 'z' I was talking about in 1b)
How many pages are there in the book
Sophia is reading a book. On the first day, she reads 1/5 of the pages plus 12 more. On the second day, she reads 1/4 of the remaining pages plus 15 pages. On the third day, she reads 1/3 of the remaining pages plus 18 pages. After this, she has 1/4 of the book left to read. How many pages are there in the book?
First, we can name each triangle:
ReplyDeleteThe triangle on the right - a
The triangle in the middle - b
The triangle on the left - c
Well if we can work out what the angle on the right is on a as we already have two of the angles. Once you work it out you get 79 and using vertical angles, you realise that the leftmost angle on c is also 79 meaning the top angle on b is 101 and the angle on the right on b is 45. This gives you 2x + 45 = 180 and x = 67.5°. This gives you y = 33.5°
1b) Well, for this one, there is a backwards 'z' with angles of 2b and 180 - 108 so angles of 2b and 72. If you have a 'z' or a backwards one, it's angles are always equal so 2b = 72 and b is 36.