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°
