Question

i need to know how angle ABC = angle PQR

Answer 1

Angle 1 = Angle 2 (i)

Angle 3= Angle 4 (ii)

Adding (i) and (ii)
Angle ABC = Angle PQR

Euclid's axiom used: If equals are added to equals, the whole is equal.

Answer 2

we know
angle 1 = angle 2 .........1
angle 3 = angle 4.........2

adding 1 and 2 we get
ang. 1 +ang. 3 = ang. 2 + ang. 4
therefore ang. ABC = ang. PQR

HENCE PROVED

hope this helps you