Question

Can someone explain this? :)

Answer 1

a) a=57° b=123° c=123°

b) f=98° d=98° e=98°

c) g=75° h=75°

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)

Answer 2

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

-------------------------

To summarize, we have these three angles

a = 123

b = 123

c = 57