In the figure, lines AB, CD and EF are parallel.Find the angles ∠x,

1.	In the figure, lines AB, CD and EF are parallel.Find the angles ∠x, ∠y, ∠z and ∠p.
Answer» ∵ AB \|\| CD \|\| EF (given) ∴ ∠y + 58° = 180° (interior angle sum) ⇒ ∠y = 180° – 58° = 122° ∴ ∠x = 180° – 122° = 58° (linear pair) Now AB \|\| CD ∠x = ∠z = 58° (alt. angles) and ∠y = ∠p= 122° (corresponding angles) Hence, x = 58°, y = 122°, z = 58°, and p = 122°.

In the figure, lines AB, CD and EF are parallel.Find the angles ∠x, ∠y, ∠z and ∠p.

Answer»

∵ AB || CD || EF (given)

∴ ∠y + 58° = 180°

(interior angle sum)

⇒ ∠y = 180° – 58° = 122°

∴ ∠x = 180° – 122°

= 58° (linear pair)

Now AB || CD

∠x = ∠z = 58° (alt. angles) and ∠y = ∠p= 122°

(corresponding angles)

Hence, x = 58°, y = 122°, z = 58°, and

p = 122°.