Question

In fig. $10.74$ diagonal AC of rectangle ABCD makes an angle of ${35}^o$ with side BC. The measure of acute angle $\angle COD$ between the diagonals is

• A. ${35}^o$
• B. ${70}^o$
• C. ${55}^o$
• D. `${45}^o$

Answer 1

The correct option is B ${70}^o$

From figure,

$\angle OBC=\angle OCB={35}^o$

And, In $△BOC$

$\angle OBC+\angle OCB+\angle BOC={180}^o$

=> ${35}^o+{35}^o+\angle BOC={180}^o$

=> $\angle BOC={180}^o-{70}^0={110}^0$

As,

=> $\angle BOC+\angle COD={180}^o$ .......(linear angle)

=> $\angle COD={180}^o-{110}^o$

=> $\angle COD={70}^o$