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As shown in the diagram angle BAC=90 degrees. Let X be the foot of the altitude from A to overline BC, AY be the bisector of angle BAC, and AZ be the median of triangle ABC. If angle XAY = 16 degrees, then what is the measure of angle ZAC in degrees?

 Jan 12, 2024

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 #1
avatar+129850 
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B

        X

                   Y

                               Z

A                                            C

 

Angle YAB  = 45

Angle XAB  =  Angle YAB - Angle XAY  =  45 - 16  = 29

 

Angle ABX  = Angle AXB - Angle XAB  =  90  - 29  =  61  = Angle ABC

 

So angle  BAC =   90 - 61  =  29  = Angle ZCA

 

And  AZ = ZC

 

So  angle ZCA = Angle ZAC  =  29 (degrees)

 

cool cool cool

 Jan 12, 2024

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