Question

a diagonal of a rectangle is inclined to one side of the rectangle at 25° . The acute angle between the diagonal is​

Answer 1

The acute angle between the diagonal is 50°.

Solution:

Let PQRS be the rectangle and the diagonals be OP = OR and OQ = OS

step-by-step explanation:

In ∆QOR

∠OQR = ∠ORQ ............... ( opposite angle of the isosceles triangle )

∠QOR + ∠OQR + ∠ORQ = 180°

⟹ ∠QOR + 25° + 25° = 180°

⟹ ∠QOR + 50° = 180°

⟹ ∠QOR = 180° - 50°

∴ ∠QOR = 130°

Now, ∠POQ + ∠QOR = 180° .............. ( linear pair )

⟹ ∠POQ + 130° = 180°

⟹ ∠POQ = 180° - 30°

∴ ∠POQ = 50°