The equilateral triangle, and regular pentagon, gives the measure of the
angles formed from which the interior angles of ABCF can be found.
Response:
The given parameters are;
The point in the regular pentagon is point F
ΔABF is an equilateral triangle
Required:
The angles in quadrilateral ABCF
Solution:
Given that ΔABF is an equilateral triangle, we have;
∠FBA = ∠BAF = ∠AFB = 60°
∠ABC = An interior angle of a regular pentagon = 108°
Which gives;
∠BCF = ∠BFC = Base angles of an isosceles triangle ΔBCF
Which gives;
∠BCF + ∠BFC + 60° + 60° + 108° = 360°, angle sum property of a quadrilateral
2·∠BCF + 60° + 60° + 108° = 360°
2·∠BCF = 360° - (60° + 60° + 108° ) = 132°
∠BCF = 132° ÷ 2 = 66°
The interior angles of quadrilateral ABCF are;
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