Let us draw a picture to determine which type of the triangle has been formed in the given scenario.
Let Gene's home is at point A, the shopping mall is at B and the library is at C. Please see the attached image.
Now, we can see that the triangle is a right angle triangle. The angle B is 90 degrees.
We know that the sum of all interior angle of a triangle is 180 degrees. Hence, we can say that
[tex]A+B+C=180^{\circ}\\A+90+C=180\\A+C=90[/tex]
It means that the sum of angles A and C should be 90 degrees. So, both the angles must be less than 90 degrees.
Hence, the largest angle made during the trip was 90 degrees.
