SOLUTION: ABCDEF is a regular hexagon. ABXY isa a square inside the hexagon. Find a. ∠XBC b. ∠BXC and c. ∠ FAX.
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Question 1164928: ABCDEF is a regular hexagon. ABXY isa a square inside the hexagon. Find a. ∠XBC b. ∠BXC and c. ∠ FAX.
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
.
The interior angles of a regular hexagon measure 180}{6}\ =\ 120^\circ)
. So angle XBC is 120 minus the right angle of the square.
Since BX and BC both measure 1, triangle BXC is isosceles. So angle BXC is (180 minus angle XBC)/2.
Angle FAY is congruent to angle XBC, and the diagonal of the square bisects the right angle YAC, so Angle FAX measures the sum of angle XBC and 45 degrees.
John
My calculator said it, I believe it, that settles it
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