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

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by Scott@TargetTestPrep » Thu Mar 21, 2019 4:40 pm
BTGmoderatorDC wrote:Image

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
Since JKLMN is a regular pentagon, each exterior angle is 360/5 = 72, so each interior angle is 180 - 72 = 108.

Triangle JKN is an isosceles triangle with vertex angle J = 108, so angle QNR = (180 - 108)/2 = 72/2 = 36. Since angle QRN = 90, angle RQN = 180 - 90 - 36 = 54. Since angle KQL and angle RQN are vertex angles, angle KQL = 54.

Answer: D

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