Question

in the diagram below, \\(\overline{ab} \cong \overline{bc}\\), and \\(\text{m}\angle a = 64^{\circ}\\). find \\(\text{m}\angle bcd\\).
step angle reason
1 \\(\text{m}\angle a = 64^{\circ}\\) given
2 \\(\text{m}\angle acb = 64^{\circ}\\) base angle of an isosceles triangle
try \\(\text{m}\angle \square = \square^{\circ}\\) select a reason

Explanation:

Step1: Identify supplementary angles

$\angle ACB$ and $\angle BCD$ are supplementary (form a straight line).

Step2: Calculate $\angle BCD$

$m\angle BCD = 180^\circ - m\angle ACB$
$m\angle BCD = 180^\circ - 64^\circ = 116^\circ$
Reason: Supplementary angles sum to $180^\circ$

Answer:

$\boldsymbol{m\angle BCD = 116^\circ}$
Reason: Supplementary angles form a straight angle