prove
m∠5+m∠2+m∠6=180°
we have that
m∠1+m∠2+m∠3=180° equation I
m∠1=m∠5 -------- > internal alternate angles equation 2
and
m∠6=m∠3-------- > internal alternate angles equation 3
I substitute equation 2 and equation 3 in equation I
m∠1+m∠2+m∠3=180°-------- > m∠5+m∠2+m∠6=180°------- > is ok