Ta có:
ˆAQB=180o−(ˆQAB+ˆQBA)AQB^=180o−(QAB^+QBA^)
=180o−ˆA+ˆB2=180o−A^+B^2
Tương tự, ta được:
ˆDPC=180o−ˆD+ˆC2DPC^=180o−D^+C^2
⇒ˆAQB+ˆDPC=180o−ˆA+ˆB2+180o−ˆD+ˆC2⇒AQB^+DPC^=180o−A^+B^2+180o−D^+C^2
⇔ˆAQB+ˆDPC=360o−ˆA+ˆB+ˆD+ˆC2=360o−360o2=180o⇔AQB^+DPC^=360o−A^+B^+D^+C^2=360o−360o2=180o
mà ˆAQB+ˆDPC=360o−(ˆQNP+ˆQMP)AQB^+DPC^=360o−(QNP^+QMP^)
⇒ ˆQNP+ˆQMP=360o−180o=180o