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In the diagram, \(\angle CBD = \angle CDB\), \(\angle ABP = 5x-7^\circ\), and \(\angle EDQ = 2x+11^\circ\). What is \(\angle ABD\) (in degrees)?

 

I got 153 but it was incorrect!

 Sep 14, 2018
edited by Lightning  Sep 14, 2018
 #1
avatar+28130 
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ABP = CBD  and EDQ = CDB so, because CBD = CDB we must have ABP = EDQ 

 

Hence 5x - 7 = 2x + 11  

           3x = 18

             x = 6°

 

Therefore ABP = 5*6 - 7 or ABP = 23°

 

ABP + ABD = 180°  so  ABD = 180 - 23  or  ABD = 157°

 Sep 15, 2018

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