Question

Help! I don't know what I did wrong on part 2. This is the clearest picture I have

Answer 1

Q. 2:

(a) Supplementary to angle 5

Recall that the supplementary angles are those which add up to 180°

Also, we know that the same side interior angles and the same side exterior angles are supplementary.

The angle 5 and angle 2 are the same side interior angles so they must be supplementary.

Also, the adjacent pairs (linear pairs) of angles are always supplementary.

So, angle 5 and angle 7 must be supplementary as well as angle 5 and angle 6.

Finally, angle 5 and angle 3 are also supplementary since angle 3 is equal to angle 2.

Summary:

The following angles are supplementary to angle 5.

∠2, ∠3, ∠6, ∠7

(b) Congruent to angle 8.

Recall that the vertically opposite angles are congruent.

Angle 8 and angle 5 are vertically opposite angles so they must be congruent.

Also, angle 8 and angle 4 are corresponding angles so they must be congruent.

Since angle 1 is vertically opposite to angle 4 and angle 4 is equal to 8 then angle 4 is also congruent to angle 8.

Summary:

The following angles are congruent to angle 8.

∠5, ∠4, ∠1

(c) By which postulate could we conclude that ∠2 ≅ ∠7?

Notice that angle 2 and angle 7 are alternate interior angles

Therefore, we can conclude that ∠2 ≅ ∠7 by the postulate of alternate interior angles.

(d) if m∠3 = 73° what is ∠7?

Notice that angle 3 and angle 7 are corresponding angles.

Since the corresponding angles are equal, ∠7 must also be 73°

$m\angle7=73\degree$