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In the figure above, JKLMN is a regular pentagon. Find the m

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In the figure above, JKLMN is a regular pentagon. Find the measure of ∠KQL

A. 45
B. 48
C. 51
D. 54
E. 60

OA D

Source: Magoosh
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by Manasa3190 » Mon Dec 31, 2018 5:43 am
From the figure,

∠KJN = 108 (interior angle of a pentagon)

Since the line KN is formed by joining opposite vertexes of a triangle ∠JKN = ∠JNK = x
Angles in a triangle = 180
∠JKN + ∠JNK = 180 - ∠KJN
2x = 180 - 108
x= 36
∠JKN = ∠JNK = 36

Given,
∠QRN = 90
and ∠QNR = 36 since ∠KJN = 36
∠RQN = 180 - 36-90
∠RQN = 54
Triangle KQL and RQN are Similar triangles
implies ∠KQL = ∠RQN = 54

Option D is correct
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