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Consider the figure below. Abraham cut regular pentagon ABCDE into quadrilateral BEGC. Which of the following statements is true about quadrilateral BEGC? (picture included)

Consider the figure below. Abraham cut regular pentagon ABCDE into quadrilateral BEGC-example-1

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Answer:3, 4, and 6

Step-by-step explanation: Trust me I took the test. Hope it helps

User Thomas Hirsch
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Let 'n' be the number of side of a regular polygon each angle are equal and sum of each angle equal to (n-2)×180.
\\∴For a regular pentagon have five equal side, n=5
\\ ∴ sum of each angle = (n-2)×180=3×180 = 540. and ecah angle = 540÷5=108°. Therefore ∠BCG = 108° and ∠ABC =108°
\\ Here BE is one of the diagonal of regular pentagon ABCDE. BE divide ∠ABC in 1:2 ratio
\\ Therefore ∠ABE : ∠CBE = 36: 72
\\∴ ∠GCB + ∠CBE = 108° +72°=180°

User Jonathan Watmough
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