Question

Diagonals of a rectangle ABCD intersect at point O. If AC=8cm then find BO and if ∠CAD=35° then find ∠ACB.

Answer 1

Answer:

BO= 4 cm

∠ACB =55°

Step-by-step explanation:

Diagonals of a rectangle ABCD intersect at point O. If AC=8cm then to find BO

We know that from the property of rectangle that,Diagonals of rectangle bisect each other.

Here AC = 8 cm

BO = 1/2 of BD= 1/2 of AC

since diagonals of rectangle are equal.

BO = 4 cm

if ∠CAD=35° then to find ∠ACB.

We know that ∠ C= 90°

∠CAD=35°

than

∠ACD=35° [ Alternate interior angles]

∠C =∠ACB+ ∠ACD

90°=∠ACB+35°

∠ACB= 90°-35°

∠ACB =55°

Hope it helps you.

Answer 2

Diagonals of a rectangle are congruent.

So, AC=BD=8 cm

Also, rectangle is a parallelogram so, the diagonals bisect each other.

Thus, BO=OD=4 cm

Now, AD∣∣CB

So, ∠CAD=∠ACB=35⁰

(Since, alternate interior angles are equal)