Answer:
x = 115°
y = 65°
z = 65°
Step-by-step explanation:
See the attached diagram.
PQ is line b and RS is line a and Line a ║ Line b.
Now, AD is line c and EH is line d and Line c║ Line d
Given that ∠ ABP = 115° and ∠ ABP and ∠ ABF are supplementary.
So, ∠ ABF = 180 - 115 = 65°
Now, ∠ ABF and ∠ y are corresponding angles as Line a ║ Line b and Line c is transverse.
So, ∠ y = 65°
Now, BFGC is a parallelogram and ∠ y = ∠ z (Opposite angles)
So, ∠ Z = 65°
Now, ∠ Z and ∠ CGF are supplementary as Line a ║ Line b and Line d is transverse.
So, ∠ CGF = 180° - 65° = 115°
Again, ∠ x = ∠ CGF {Vertically opposite angles}
⇒ ∠ x = 115° (Answer)
