Question

find x in the following figure​

Answer 1

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Answer 2

$\large{\bf{\underline{{Given}:-}}$

• ∠KEA = 90°

• ∠LDE = 60°

• ∠PBN = 40°
• ∠EAB = 90°

• ∠MAB = ∠1

$\large{\bf{\underline{{To\: Find}:-}}$

• ∠LCP = ∠x

$\large{\bf{\underline{{Explanation}:-}}$

➤ On Line KL,                

↦ ∠KEA + ∠DEA = 180°    [Linear Pair]

↦  90° + ∠DEA = 180°

↦ ∠DEA = 180° − 90°

↦ ∠DEA = 90°

➤ On Line LC,          

↦ ∠CDE + ∠LDE = 180°     [Linear Pair]

↦ ∠CDE + 60° = 180°

↦ ∠CDE  = 180° − 60°

↦ ∠CDE = 120°

➤ ON Line AN,            

↦ ∠ABC + ∠PBN = 180°    [Linear Pair]

↦ ∠ABC + 40° = 180°

↦ ∠ABC = 180° − 40°

↦ ∠ABC = 140°

➤ In Pentagon ABCDE,

↦ ∠ABC + ∠CDE + ∠DEA + ∠EAB + ∠BCD = 540°

↦ 140° + 120° + 90° + 90° + ∠BCD = 540°

↦ 440° + ∠BCD = 540°

↦ ∠BCD = 540° − 440°

↦ ∠BCD = 100°

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➤ On Line BP,

↦ ∠BCD + ∠LCP = 180°      [Linear Pair]

↦  100° + ∠x = 180°  

↦  ∠x = 180° − 100°

↦  ∠x = 80°  

Hence, The value of 'x' in the following figure is 80°.

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