Let 'x', 'y' and 'z' represent the measures of the triangle's angles and x is the smallest.

Since the angles of triangle add up to 180 degrees we have:

x + y + z = 180

The measure in degrees of one angle of a triangle is 110 greater than that of another:

y = 110 + x

The measure of the third is 14 greater than twice that of the smallest:

z = 14 + 2x

We have the following system of equations:

x + y + z = 180

y = 110 + x

z = 14 + 2x

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x = 14 degrees

y = 124 degrees

z = 42 degrees

The angles of the triangle are 14 degrees, 124 degrees and 42 degrees.