Answer:
#2
CD ║ EF and ED is transversal, hence
- ∠CDE ≅ ∠FED ⇒ m∠CDE = m∠FED ⇒ m∠CDE = 28° as alternate interior angles
- m∠CDB = 160° - 28° = 132°
We can see that:
- m∠CDB + m∠ABD = 132° + 48° = 180°
Since the angles CDB and ADB sum to 180, these are consecutive interior angles, therefore AB and CD are parallel lines.
#3
PU and QT are parallel and PT is transversal, therefore:
- ∠UPT ≅ ∠QTP as alternate interior angles
- m∠UPT = m∠QTP = 42° or x = 42°
Now find the missing angles of ΔQTP
- x + 40° = 42° + 40° = 82°
- y = 180° - (42° + 82°) = 56°
Now, we see that:
As ∠TPQ ≅ ∠SQR these angles are corresponding angles.
Therefore PT and SQ are parallel lines.
