Question

EF and GH are parallel lines intersected by transversal I at points A and B respectively.

Answer 1

If <1= 45°, then <3=45° (vertically opp. Angles.)
<3=<5 (Alternative angles.)
So, <5=45°
<3+<2=180° ( Linear pair)
45°+<2=180°
<2=180-45= 135°
<2=<4 (Vertically oppo. Angles)
So, <4=135°
<2=<6 (Alternative angles)
<6= 135°
<6+<7=180° (Linear pair)
<7= 45°
<6=<8(Vertcally opposite angles)
<8= 135°, <5=45°
Thnkx from @Dhillonrobin

Answer 2

angle 1 + angle 4 = 180° (linear pair)
45° + angle 4 = 180°
angle 4 = 180° - 45°
= 135°
similarly,
angle 3= angle1 ( v.o.a.)
= 45°
angle 2 = angle 4 (v.o.a.)
= 135°
angle 5 = angle 3 (alternate angle)
= 45°
angle 6 = angle 4 (alternate angle)
= 135°
Angle 7= angle 5 (v.o.a.)
= 45°
angle 8 = angle 6 (v.o.a.)
= 135°