Question 1151143
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From the condition, segment DG is congruent to segment DC.


So the triangle DGC is isosceles.


The angle GDC of this triangle is  60° + 90° = 150°.


Therefore, the two angles  DGC  and  DCG  are congruent as the base angles of the isosceles triangle GDC

and have measure  {{{(180^o-150^o)/2}}} = 15°  each.


Then the angle DHG is the complement of the angle DGH, since these angles are the acute angles in the right angled triangle DHG.


Thus the angle DHG  is  75°.      <U>ANSWER</U>
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Solved.