<PRE><B>Question 1102351</B>
&lt;br&gt;
Let E be the midpoint of side AB, so that DE is the perpendicular bisector of AB.&lt;br&gt;
Then triangle ABD is isosceles; and triangles AED and BED are congruent.&lt;br&gt;
Let F be the point where BC and DE intersect.&lt;br&gt;
Let x be the measure of angle ABC that we are looking for.  Then&lt;br&gt;
angle BFE is 90-x  [complement of x]
angle BFD is 90+x  [supplement of angle BFE]
angle BDF is 74-x  [angle sum of triangle BDF, given that angle DBC is 16]&lt;br&gt;
angle ACB is 118  [given]
angle BCD is 62   [supplement of ACB]
angle CFD is 90-x [vertical angle to BFD]
angle CDF is x+28 [angle sum of triangle CFD]&lt;br&gt;
But angles BDF and CDF are corresponding angles in congruent triangles AED and BED, so
{{{74-x = x+28}}}
{{{46 = 2x}}}
{{{x = 23}}}&lt;br&gt;
The measure of angle ABC is 23 degrees.&lt;br&gt;
There might well be easier ways to get to this result....  The above is what I came up with.
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