Question

In a parallelogram ABCD. If $AC>BD$, then $\angle ABC$ is

• A. Acute
• B. Obtuse
• C. Right angle
• D. Reflex

Answer 1

The correct option is B Obtuse

$AC>BD$
$AO>OB$
$\therefore \angle x>\angle m$
$and\angle y>\angle n$
$\therefore \angle x+\angle y>\angle m+\angle n$
$Now,2(\angle x+\angle y+\angle m+\angle n)={360}^o$
$or2(\angle x+\angle y+\angle x+\angle y)>{360}^o$
$or2\times 2(\angle x+\angle y)>{360}^o$
$or\angle x+\angle y>{90}^o$
Hence, $\angle ABC$ is obtuse.