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Point D is on side AC of triangel ABC such that angle ADB = angle ABD and angle ABC - angle ACB = 37 degrees. Find angle DBC in degrees.

 Aug 4, 2022
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                  A

                            D

 B                                C

 

Angle ACB   = x

Angle ABC  = x + 37

 

Angle  A  =   180  - (2x + 37)  =  143 - 2x

 

And since angle  ABD  = angle ADB  then the measure of each of thee angles = (143 -2x)  / 2 

So angle  BDC =  180  - (143-2x)/2

And angle  DBC  = angle ABC  - angle ABD  =    (x + 37) - (143 -2x)  / 2

 

So in triangle BDC

 

ACB + BDC + DBC   =180

 

x  +  180 - (143 -2x)  / 2   + (x + 37)  - (143 -2x) / 2   =  180

 

Simplifying this we get

 

4x + 74 =  180

 

4x  = 106

 

x = 106/4  =  53 / 2   =  26.5°

 

So angle DBC  =     (26.5 + 37) - (143 - 2(26.5) ) / 2  =    18.5°

 

 

cool cool cool

 Aug 4, 2022

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