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°
