Question

1. $overline{bc}$ bisects $angle acd$

$mangle1 = $
$mangle2 = $
$mangle3 = $
$mangle4 = $

Explanation:

Step1: Find $m\angle2$

$\angle2$ is a right angle, so $m\angle2 = 90^\circ$

Step2: Calculate $m\angle1$

Sum of $\triangle ABC$ angles is $180^\circ$.
$m\angle1 = 180^\circ - 48^\circ - 90^\circ = 42^\circ$

Step3: Find $m\angle3$

$\overline{BC}$ bisects $\angle ACD$, so $\angle3=\angle2$.
$m\angle3 = 90^\circ$

Step4: Calculate $m\angle4$

Sum of $\triangle BCD$ angles is $180^\circ$.
$m\angle4 = 180^\circ - 90^\circ - 83^\circ = 7^\circ$

Answer:

$m\angle1 = 42^\circ$
$m\angle2 = 90^\circ$
$m\angle3 = 90^\circ$
$m\angle4 = 7^\circ$