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**0 **

15 Degrees

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

You are very welcome!

:P

CoolStuffYT Nov 6, 2018

#3**+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°

CPhill Nov 6, 2018