Shapovalov A.V.

Through the origin, lines (including the coordinate axes) are drawn that divide the coordinate plane into angles of $1^{\circ}$.

Find the sum of the abscissas of the points of intersection of these lines with the line $y=100-x$.

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The picture is symmetric with respect to the line $y=x$, so the sum of the abscissas is equal to the sum of the ordinates. Through the origin, 180 lines are drawn, the line $y=100-x$ intersects 179 of them. For each point on the line $y=100-x$, the sum of the coordinates is 100, therefore, the total sum of the abscissas and ordinates is 17900, and the sum of the abscissas is half of that.

## Answer

8950.