First, find using exterior angle theorem.

Since , and forms a straight line.

So,

                (Add: )

                             (Subtract 116 from each side)

Next, find .

The sum of the measures of the angles of a triangle is 180.

      (Angle sum theorem)

          (Substitute )

                 (Add: )

                              (Subtract 127 from each side)

The measure of is 53.