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Geometry Level 1

Δ \Delta A B M ABM is Equilateral Triangle and A B C D ABCD is Square, then find D M C \angle DMC (in degrees).


The answer is 150.

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2 solutions

Roger Erisman
Dec 15, 2018

MAB = 60 = MBA. Eq triangle

DAM = CBM = 30. Rt angle - 60

BCM = ADM = 75. Base angle of isosceles triangle( 180 - 30)/2

CDM = DCM = 15. Rt angle - 75

DMC = 150. 180 - 2*15

X X
Aug 1, 2018

M A B = 6 0 , D M A = 3 0 , A M D = 18 0 3 0 2 = 7 5 , D M C = 36 0 7 5 6 0 7 5 = 15 0 \angle MAB=60^\circ,\angle DMA=30^\circ,\angle AMD=\frac{180^\circ-30^\circ}{2}=75^\circ,\angle DMC=360^\circ-75^\circ-60^\circ-75^\circ=150^\circ

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