Question

Pleaseee helppp!!!!!

Answer 1

x = 115°

y = 65°

z = 65°

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)