Question

I know how to solve number 4 but I’m having a hard time with 1,2,3,5,6

Answer 1

Part 1)
angle b=112-------> by vertical angles
angle a+112=180-----> supplementary angles
angle a==180-112----> angle a=68
angle c=angle a-----> by vertical angles
angle c=68

the answer part 1) is

angle a=68°
angle b=112°
angle c=68°

part 2)
angle a+15+38=180-----> angle a=180-(15+38)----> angle a=127

the answer part 2) is
angle a=127°

part 3)
angle b=40-----> by vertical angles
angle d=70-----> by vertical angles
2*angle x+40+angle d=180----> 2*angle x=180-(40+70)
2*angle x=70------> angle x=35
angle a=angle x-----> by vertical angles
angle a=35
angle c=angle x-----> by vertical angles
angle c=35

the answer part 3) is
angle a=35°
angle b=40°
angle c=35°
angle d=70°

Part 4)
angle a+70=90------> are complementary angles
angle a=90-70----> angle a=20
angle a+angle b=90----> are complementary angles
angle b=90-angle a----> 90-20-----> angle b=70
angle d=70 -------> by vertical angles
angle d+angle e=180------> supplementary angles
angle e=180-angle d----> angle e=180-70----> angle e=110
angle a+angle b+angle c+angle d=180
angle c=180-(20+70+70)----> angle c=20

the answer part 4) is
angle a=20°
angle b=70°
angle c=20°
angle d=70°
angle e=110°

Part 5)
angle a+90=180------> supplementary angles
angle a=180-90----> angle a=90
angle a +angle b=180----> supplementary angles
angle b=180-angle a----> angle b=180-90----> angle b=90
angle e=132-----> by vertical angles
angle d+132=180-----> supplementary angles
angle d=180-132----> angle d=48
angle c+138=180-----> supplementary angles
angle c=180-138----> angle c=42

the answer part 5) is
angle a=90°
angle b=90°
angle c=42°
angle d=48°
angle e=132°

part 6)
angle a+110=180------> supplementary angles
angle a=180-110----> angle a=70
angle c=25-----> by vertical angles
angle b+100+25=180----> angle b=180-(100+25)----> angle b=55

the answer Part 6) is
angle a=70°
angle b=55°
angle c=25°