Question

point f is inside regular pentagon abcde so that triangle abf is equilateral. Find all the angles of abcf, in degrees

Answer 1

The equilateral triangle, and regular pentagon, gives the measure of the

angles formed from which the interior angles of ABCF can be found.

Response:

• ∠BCF = 66°

• ∠BAF = 60°

• ∠CFA = 126°

• ∠ABC = 108°

Which properties of figures can be used to find the interior angles?

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;

• ∠FBC = 108° - 60° = 48°

∠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;

• ∠BCF = 66°

• ∠BAF = 60°

• ∠CFA = 66° + 60° = 126°

• ∠ABC = 108°

Learn more about pentagons here:

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