ABCDE is a regular pentagon as shown in the given figure. Find the value of x, y and z.
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In 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°
In 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°
TwilightSky:
Could you explain? In BDE, the angles are z, y and e. the answer is unclear.
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This is absolutely correct answer
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