Question

How do I solve for letters, A, B, C, D, E, F, G?

Answer 1

Answer:

 a=41°

 b=32°

 c=58°

 d=65°

 e=57°

 f=56°

 g=80°

Step-by-step explanation:

In ΔCOD,

g+58°+42°=180°              [Angle sum propery of triangle]

g=180°-100°

g=80°

c=58°                           [vertically opposite angles]

In ΔAOF,

c+b+90°=180°               [angle sum property]

58°+90°+b=180°             [c=58, v.o.a]

b=180°-148°

b=32°

d=65°                         [vertically opposite angles]

In ΔABO

74°+d+a=180°               [angle sum property]

74°+65°+a=180°             [d=65, v.o.a]

a=180°-139°

a=41°

58°+65°+∠EOF =180°   [linear pair]

∠EOF=180°-123°

∠EOF=57°

e=57°=∠EOF              [vertically opposite angles]

In ΔBCO,

67°+f+e=180°              [angle sum property]

67°+f+57°=180°

f=180°-124°

f=56°

∴a=41°

 b=32°

 c=58°

 d=65°

 e=57°

 f=56°

 g=80°