Question

In the given figure, DREAM is a regular pentagon. The bisector of
angleMDR meets AE at Q. If the bisector of angleAER meets QD at P,
find angleEPQ​

Answer 1

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8th

Maths

Understanding Quadrilaterals

Angle Sum Property

ABCDE is regular pentagon. ...

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Asked on December 30, 2019 by

Gurram Sagani

ABCDE is regular pentagon. The bisector of ∠A of the pentagon meets the side CD in M. Then the measure ∠AMC is

MEDIUM

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ANSWER

Each interior angle of a regular pentagon =

n

2n−4

×90

=

5

2×5−4

×90

0

=6×18=108

0

∴∠BAM=

2

1

(108

0

)=54

0

In the quadrilateral ABCM,

∠BAM+∠ABC+∠BCM+∠AMC=360

0

⇒54

0

+108

0

+108

0

+∠AMC=360

0

⇒∠AMC=90

0