SOLUTION: In the diagram to the bottom, ABCD and DEFG are congruent squares. Find the measure of angle DHG. Diagram: https://imgur.com/a/vPODiDB

Algebra ->  Angles -> SOLUTION: In the diagram to the bottom, ABCD and DEFG are congruent squares. Find the measure of angle DHG. Diagram: https://imgur.com/a/vPODiDB      Log On


   

Question 1151143: In the diagram to the bottom, ABCD and DEFG are congruent squares. Find the measure of angle DHG.
Diagram: https://imgur.com/a/vPODiDB
Answer by ikleyn(52855) About Me  (Show Source):
You can put this solution on YOUR website!
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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  %28180%5Eo-150%5Eo%29%2F2 = 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°.      ANSWER

Solved.