Question

Construct a rectangle with length $8cm$ and breadth $4cm$. Then the acute angle made by the diagonals is:

• A. ${68}^{\circ }$
• B. ${90}^{\circ }$
• C. ${45}^{\circ }$
• D. ${53}^{\circ }$

Answer 1

The correct option is D ${53}^{\circ }$

$\Rightarrow$ We know that opposite sides of rectangle are parallel and equal.

$\Rightarrow$ All four angle of rectangle is ${90}^{\circ }$

$\Rightarrow$ So, by using these properties we will draw a rectangle.

$\Rightarrow$ Draw a line segment AB = 8cm.

$\Rightarrow$ Construct an angle of ${90}^{\circ }$ at points A and B.

$\Rightarrow$ Cout off AD = 4cm and BC = 4cm.

$\Rightarrow$ Join CD, AC and BD.

$\Rightarrow$ Thus, ABCD is a required rectangle.

$\Rightarrow$ We have to measure acute angles between the diagonals which are $\angle AOD$ and $\angle BOC$

$\Rightarrow$ $\angle AOD=\angle BOC={53}^{\circ }$.