Question

Given: KLMN is a parallelogram, LF is perpendicular to KN, LD is perpendicular to NM, angle FLD = 35. Find angles of KLMN

Answer 1

m∠K= 35°, m∠KLM= 145°, m∠M= 35°, m∠N = 145°

Explanation:

Answer 2

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°