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In rectangle ABCD, we have AD = 3 and AB = 4. Let M be the midpoint of AB, and let X be the point such that MD = MX, angle MDX = 79 degrees, and A and X lie on opposite sides of DM. Find angle XCD, in degrees.

 

 Oct 31, 2020
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Draw a straight line from point M to point C.

 

∠CMB = ∠MCD = arctan(3 / 2) = 56.30993247º

 

∠DMX = 180 - 2 * 79 = 22º

 

∠CMX = 180 - [(2*∠CMB) + 22] = 45.38013505º

 

∠MCX = 1/2 (180 - ∠CMX ) = 67.30993247º

 

∠XCD = ∠MCX - ∠MCD = 11º  smiley

 Oct 31, 2020
edited by jugoslav  Oct 31, 2020

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