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1. Given that \(DJ \parallel KE\), \(\angle DBF = 37^\circ\), and \angle \(ABC = 46^\circ\), find \(\angle GCE\) (in degrees). 

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


 

Guest Oct 24, 2017
edited by Guest  Oct 24, 2017

Best Answer 

 #2
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∠GCE  =  ∠CBJ      because they are corresponding angles.

 

And

 

∠CBJ  and  ∠DBF  are vertical angles, so  ∠CBJ  =  ∠DBF

 

∠DBF  =  37º

 

So...     ∠GCE  =  ∠CBJ  =  ∠DBF  =  37º

 

----------

 

∠ABP  and  ∠CBD  are vertical angles, so  ∠ABP  =  ∠CBD

 

From the information given, ∠CBD  =  ∠CDB

 

∠CDB  and  ∠EDQ  are vertical angles, so  ∠CDB  =  ∠EDQ

 

So....     ∠ABP  =  ∠CBD  =  ∠CDB  =  ∠EDQ

 

∠ABP  =  ∠EDQ

5x - 7  =  2x + 11

3x  =  18

x  =  6

 

So we know...      ∠ABP  =  5x - 7  =  5(6) - 7  =  23°

 

∠ABD  and  ∠ABP  form a straight line, so  ∠ABD + ∠ABP  =  180°

 

∠ABD + 23°  =  180°

 

∠ABD  =  180° - 23°  =  157°

hectictar  Oct 24, 2017
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 #1
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Only need help with 1 now

Guest Oct 24, 2017
 #2
avatar+5237 
+1
Best Answer

∠GCE  =  ∠CBJ      because they are corresponding angles.

 

And

 

∠CBJ  and  ∠DBF  are vertical angles, so  ∠CBJ  =  ∠DBF

 

∠DBF  =  37º

 

So...     ∠GCE  =  ∠CBJ  =  ∠DBF  =  37º

 

----------

 

∠ABP  and  ∠CBD  are vertical angles, so  ∠ABP  =  ∠CBD

 

From the information given, ∠CBD  =  ∠CDB

 

∠CDB  and  ∠EDQ  are vertical angles, so  ∠CDB  =  ∠EDQ

 

So....     ∠ABP  =  ∠CBD  =  ∠CDB  =  ∠EDQ

 

∠ABP  =  ∠EDQ

5x - 7  =  2x + 11

3x  =  18

x  =  6

 

So we know...      ∠ABP  =  5x - 7  =  5(6) - 7  =  23°

 

∠ABD  and  ∠ABP  form a straight line, so  ∠ABD + ∠ABP  =  180°

 

∠ABD + 23°  =  180°

 

∠ABD  =  180° - 23°  =  157°

hectictar  Oct 24, 2017
 #3
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Thanks!!!

Guest Oct 24, 2017

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