The task is: Given a triangle with identical lines, in this way as you can see on the picture. The orange lines are the same. Calculate !
is an isosceles triangle, therefore .
The sum of the angles at the B point is , because AH is a line:
From the isosceles triangles and the sum of angles at the C point:
Same way , because if we see an angle:
This is true for the first, second and third angles, so this must be true for every angles.
If we have a triangle with lines, then the last is the th.
Now in the bottom triangle: or generally . But if we see the big triangle . Therefore . After substituting: . Replacing :
Now can you solve this?