Question

The acute angle made by the diagonals is:

• A. ${74}^{\circ }$
• B. ${63}^{\circ }$
• C. ${37}^{\circ }$
• D. ${16}^{\circ }$

Answer 1

The correct option is A ${74}^{\circ }$

$\Rightarrow$ We know the properties of rectangle that, its opposite sides are equal and parallel.

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

$\Rightarrow$ So, by using these properties we are going to construct rectangle.

$\Rightarrow$ We have given one of it's side 4cm and diagonal 5cm.

$\Rightarrow$ Draw a line segment AB = 4cm.

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

$\Rightarrow$ Cut off AC = 5cm.

$\Rightarrow$ Take A as a center and radius same as side BC and cut of AD.

$\Rightarrow$ Join AC, BD and CD.

$\Rightarrow$ We have to measure an acute angle between diagonals.

$\therefore$ $\angle AOD=\angle BOC={74}^{\circ }$