Question

3. A diagonal of a rectangle is inclined to one side of the rectangle at 25. The acute angle between the
diagonals is
(a) 55
(b) 50
(c) 40
(d) 25​

Answer 1

In △BOC,

∠OBC=∠OCB ----- (Opposite angle of isosceles triangle)

∠OBC+∠OCB+∠BOC=180

∘

25

∘

+25

∘

+∠BOC=180

∘

Therefore, ∠BOC=130

∘

So, ∠AOB+∠BOC=180

∘

--------(Linear pair)

∠AOB=180

∘

−130

∘

∠AOB=50

∘

So, the acute angle between the diagonal is 50

∘

.