Question

Can someone explain this? :)

Answer 1

I'll do part (a) to get you started.

The angle 'a' pairs up with the 123 degree angle as a corresponding angle pair. Due to the parallel lines, the corresponding angles are congruent. Therefore a = 123.

We also see that b = 123 as well since a = b (they are vertical angles).

Notice how angle c is adjacent to the 123 degree angle. These two angles form a straight line, so they must add to 180 degrees.

c+123 = 180

c = 180-123

c = 57

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To summarize, we have these three angles

a = 123

b = 123

c = 57

Answer 2

Answer:

a)      a=57°    b=123°   c=123°

b)     f=98°  d=98°   e=98°

c)     g=75°    h=75°

Step-by-step explanation:

a) a°+123°=180°  (angle on a straight line=180°)

    a°=180°-123°

     a°=57°

  b°=123°  (alternative angles)

  c=123°   (vertically opposite angles are equal)

b)f+82°=180°  (angle on a straight line=180°)

   f=180°-82°

   f=98°

  f=d (corresponding angles are equal)

   d=e  (vertically opposite angles are equal)

c)  h=75°  (corresponding angles are equal)

    g=h  (vertically opposite angles are equal)