Question

Ifn figure ABCDE is a regular pentagon. Then find relation between a , b , c. Posted by Abhishek A. Chaudhri(student)

Answer 1

each angle in regular pentagon=108° ∠x+∠b+∠c=180° (∵ angle sum property) ∠x= 108°-∠a, 108°-∠a+∠b+∠c=180° ⇒ ∠a+∠b+∠c=72°

Answer 2

n ΔBDE, ∠b + ∠c + ∠x = 180° [Angle sum property of triangle] →(1) Also each angle of a regular pentagon is 108° Hence ∠a + ∠x = 108° ⇒ ∠x = 108° – ∠a ∴ Equation (1) becomes, ∠b + ∠c + 108° – ∠a  = 180°⇒ ∠b + ∠c – ∠a  = 180° – 108° = 72°