A train is going on a journey. First it travels east for 50 kilometers. Then it turns north and travels for 22
kilometers. Next it goes west for 50 kilometers. Finally, it travels south for a certain number of kilometers. At
the end of its journey it is back at its original location. How many kilometers did it travel in the southward
direction?

The train travel 20 kilometers in the southward direction to reach its original location.

Step-by-step explanation:

          The given is,

                First train travels east for 50 kilometers, then

                Turns north and travels for 22 kilometers

                 It goes west for 50 kilometers

Step:1

       Let, A - Distance of train travels from its starting point in Eastern direction at pq point

              B - Distance train travels in northward direction at qr point

              C - Distance of train travels in western direction at rs point

              D - Distance of train travels in southward direction to reach its starting location at sp point

Step:2

           Refer the attachment,

           Distance of travel in northward direction and distance of travel in southward direction are equal.

           qr = sp.............. (1)                           ( ∵ Eqn (1) from the Diagram)

           20 km = 20 km

          sp = 20 km

Result:

       So, the distance of train travel to reach its original location in southward direction is 20 km.

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step-by-step explanation:

answer: option a.

step-by-step explanation:

you know that the quadrilateral opqr ( a four sided figure) is inscribed in circle. this means that all its vertices are on the circle.

then, by definition, the opposite angles of the quadrilateral are supplementary, this means that the sum of their measures is 180 degrees.

you can observe in the figure that the angles ∠opq   and the angle ∠orq   are opposite, therefore:

then, can be used to d to calculate the measure of ∠opq