7

Part of 2017 Novosibirsk Oral Olympiad in Geometry

Problems(1)

sum of angles <1100^o, driver + fence (2017 Novosibirsk Oral Geo Oly 8-9 p7)

Source:

A car is driving along a straight highway at a speed of

60

km per hour. Not far from the highway there is a parallel to him a

100

-meter fence. Every second, the passenger of the car measures the angle at which the fence is visible. Prove that the sum of all the angles he measured is less than

1100^o