Question

KLMN - parallelogram LF ⊥ KN , LD ⊥ NM m∠FLD = 35° Find: Angles of KLMN

Answer 1

The question is four parts, It is required the angles of parallelogram KLMN

So, It is required ⇒ ∠K  , ∠L  , ∠M  and ∠N
See the attached figure which represents the explanation of the problem
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Part (1): Find  ∠N:
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in the shape FLDN
∵ LF ⊥ KN  ⇒⇒⇒ ∴ ∠LFN = 90°
∵ LD ⊥ NM ⇒⇒⇒ ∴ ∠LDN = 90°
∵ The sum of all angels of FLDN = 360°
∵ ∠FLD = 35°
∴ ∠FLD + ∠LDN + ∠DNF + ∠LFN = 360°
∴ 35° + 90° + ∠DNF + 90° = 360°
∴ ∠DNF = 360° - ( 90° + 90° + 35°) = 360° - 215° = 145°

∴ The measure of angle N = 145°
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Part (2): Find  ∠M:
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∵ KLMN is parallelogram , ∠N = 145°
∴ The angles N and M are supplementary angles ⇒ property of the parallelogram
∴ ∠M + ∠N = 180°
∴ ∠M = 180° - ∠N = 180° - 145° = 35°

∴ The measure of angle M = 35°

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Part (3): Find  ∠L:
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∵ KLMN is parallelogram , ∠M = 35°
∴ The angles N and M are supplementary angles ⇒ property of the parallelogram
∴ ∠M + ∠KLM = 180°
∴ ∠KLM = 180° - ∠M = 180° - 35° = 145°
OR ∠KLM = ∠N = 145° ⇒⇒⇒  property of the parallelogram

∴ The measure of angle KLM = 145°
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Part (4): Find  ∠K:
==============∵ KLMN is parallelogram , ∠N = 35°
∴ The angles N and M are supplementary angles ⇒ property of the parallelogram
∴ ∠K + ∠N = 180°
∴ ∠K = 180° - ∠N = 180° - 145° = 35°
OR ∠K = ∠M = 35° ⇒⇒⇒  property of the parallelogram

∴ The measure of angle K = 35°