In Fig, lines l1 and l2 intersect at O, forming angles as shown in t

1.	In Fig, lines l1 and l2 intersect at O, forming angles as shown in the figure. If x = 45°, find the values of y, z and u.
Answer» Given that, ∠x = 45° From the figure we can write as ∠x = ∠z = 45° Also from the figure, we have ∠y = ∠u From the property of linear pair we can write as ∠x + ∠y + ∠z + ∠u = 360° 45° + 45° + ∠y + ∠u = 360° 90° + ∠y + ∠u = 360° ∠y + ∠u = 360° – 90° ∠y + ∠u = 270° ∠y + ∠z = 270° 2∠z = 270° ∠z = 135° Therefore, ∠y = ∠u = 135° So, ∠x = 45°, ∠y = 135°, ∠z = 45° and ∠u = 135°

In Fig, lines l1 and l2 intersect at O, forming angles as shown in the figure. If x = 45°, find the values of y, z and u.

Answer»

Given that, ∠x = 45°

From the figure we can write as

∠x = ∠z = 45°

Also from the figure, we have

∠y = ∠u

From the property of linear pair we can write as

∠x + ∠y + ∠z + ∠u = 360°

45° + 45° + ∠y + ∠u = 360°

90° + ∠y + ∠u = 360°

∠y + ∠u = 360° – 90°

∠y + ∠u = 270°

∠y + ∠z = 270°

2∠z = 270°

∠z = 135°

Therefore, ∠y = ∠u = 135°

So, ∠x = 45°, ∠y = 135°, ∠z = 45° and ∠u = 135°