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in triangle ABC, a point D is on line AC so that AB=AD and angle ABC- angle ACB=32 degrees. Find angle DBC in degrees.

 Nov 23, 2019
 #1
avatar+105476 
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Since AB  = AD, let  angles ADB  and ABD  =  x

And  let  angle DAB   =  angle CAB  =  z

Let angle DBC   = y

And let angle  ABC  =  x+ y

Andl let angle  ACB  =  x + y  - 32

 

So...we have the following equations :

 

(x + y ) + [ (x + y)  - 32]  + z   = 180   ⇒    2x + 2y  + z  = 212  ⇒   (2x + z)  + 2y  =  212     (1)

 

2x + z  = 180     (2)

 

Sub (2)  into (1)   and we have that

 

180 + 2y = 212

 

2y = 32

 

y  = 16°   = angle  DBC

 

 

cool cool cool

 Nov 23, 2019
edited by CPhill  Nov 23, 2019
 #2
avatar+27 
0

thank you!

xxJenny1213xx  Nov 23, 2019

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