Question

quadrilateral abcd is a rhombus. what is $m\angle abd$?
$m\angle abd =$ ______°

Explanation:

Step1: Recall rhombus properties

In a rhombus, opposite sides are parallel, so $AB \parallel CD$, and all sides are equal ($AB = AD$). Also, consecutive angles are supplementary.

Step2: Find $\angle BAD$'s supplement

$\angle A = 72^\circ$, so adjacent angle $\angle ABC = 180^\circ - 72^\circ = 108^\circ$.

Step3: Diagonal bisects rhombus angle

Diagonal $BD$ bisects $\angle ABC$, so $\angle ABD = \frac{1}{2}\angle ABC$.
$\angle ABD = \frac{1}{2} \times 108^\circ = 54^\circ$

Answer:

$54$