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 .
I can't explain becuase I don't really know LaTeX... oh well.
You are very welcome!
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°