Question

Consider a square ABCD that has a diagonal BD. What will be the measure of each angle of the $△ABD$ formed?

• A. $\angle ABD=40°$
  $\angle BDA=40°$
  $\angle DAB=100°$
• B. $\angle ABD=55°$
  $\angle BDA=35°$
  $\angle DAB=90°$
• C. $\angle ABD=40°$
  $\angle BDA=50°$
  $\angle DAB=90°$
• D. $\angle ABD=45°$
  $\angle BDA=45°$
  $\angle DAB=90°$

Answer 1

The correct option is D $\angle ABD=45°$

$\angle BDA=45°$
$\angle DAB=90°$
We know that each angle of a square is 90°.
Also the diagonal of a square bisects the angles at its vertices.

$\therefore \angle ABD=\angle DBC=\angle CDB=\angle BDA=45°$

Hence, the measure of the angles of the triangle $△ABD$ is
$\angle ABD=45°$
$\angle BDA=45°$
$\angle DAB=90°$