Question

ABCD is a rhombus in which the altitude from D to side AB bisects AB. Then $\angle$A and $\angle$B respectively, are __________.

• A. ${60}^o,{120}^o$
• B. ${120}^o,{60}^o$
• C. ${80}^o,{100}^o$
• D. ${100}^o,{80}^o$

Answer 1

Answer: (A)

${60}^o,{120}^o$

$\angle ADE=\angle EDB=\alpha \left(say\right)$

$\angle ADB=\angle ABD=2\alpha$

from triangle EDB

$\alpha +2\alpha +{90}^{\circ }={180}^{\circ }$

$\alpha ={30}^{\circ }$

$\angle B=\angle ABD+\angle DBC=2\angle ABD$ since $\angle ABD=\angle DBC$

$\angle B=4\alpha ={120}^{\circ }$

from the triangleADE,

$\angle A+\alpha +{90}^{\circ }={180}^{\circ }$
$\angle A={60}^{\circ }$