Question

Given that ∆ABC is an equilateral triangle of side 1cm , ∆BDC is iscoceles triangle with DB = DC outward of ∆ABC and angle BDC =120 . If points M and N are on AB and AC respectively such that angle MDN =60. find perimeter of ∆AMN

Answer 1

AnswGiven, ABC is an equilateral

BDC is an isosceles right triangle

angle CBD = angle BCD = x ( angles of isosceles triangle)

In triangle BDC

x + x + angle D = 180 ( angle sum property)

2x = 180 - 90

x = 90/2

x = 45

IN triangle ABC

angle ABC = 60 ( angles of an equilateral are equal to 60)

angle ABD = x + angle ABC

Angle ABD = 45+60

Angle ABD = 105

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