Question

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 1

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°