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In the diagram shown here (which is not drawn to scale), suppose that  triangle ABC ~ triangle PAQ and triangle ABQ ~ QCP If angle BAC= 70 degeees, then compute measure of angle PQC .

EmperioDaZe  Nov 6, 2018
 #1
avatar+107 
+1

15 Degrees

 

I can't explain becuase I don't really know LaTeX... oh well.

 

You are very welcome!

:P

CoolStuffYT  Nov 6, 2018
 #2
avatar+24 
+2

Thanks!

EmperioDaZe  Nov 6, 2018
 #3
avatar+91213 
+2

ΔABC ~ ΔPAQ 

ΔABQ  ~ ΔQCP

 

angle BAC  = angle APQ  = 70

 

So angle QPC = 180 - 70 =   110

So angle AQB  =  110

 

And angle PCQ  = angle QBA

But angle QBA  = angle CBA

And angle PCQ = angle  ACB

 

So triangle ABC is isosceles  with angle CBA = angle ACB

So...one of these angles  =  [ 180 - angle BAC] / 2  =  [ 180 - 70 ] / 2  =  110 / 2   =  55

 

So...angle   PQC =  180 - angle QPC - angle  PCQ  =  180 - 110 -  55 =  180 - 165 =  15°

 

 

cool cool cool

CPhill  Nov 6, 2018
 #4
avatar+24 
+2

Thanks a lot!

EmperioDaZe  Nov 6, 2018

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