Answer: See below
Step-by-step explanation:
From the figure attached below,
We know that by the SSS property, the two triangles are congruent
[tex]$Since,$\begin{aligned}&A D=A B(\text {Given}) \\&C D=B C(\text {Given}) \\&A C=A C \text { (Common side})\end{aligned}$Hence,$\triangle A B C \cong \triangle A C D$By the properties of congruence,$\angle O A D=\angle O A B=40^{\circ}$$\angle B=\angle D$[/tex]
Using the property of congruence to find the measure of all these angles:
Therefore, the measure of the angles are:
[tex]&a) \ B\widehat{ A} C=40^{\circ} \\ b) \ &B\widehat{C}A=180^{\circ}-\left(90^{\circ}+60^{\circ}\right)=30^{\circ} \\c) \ &A \widehat{D} C=60^{\circ}+50^{\circ}=110^{\circ}[/tex]
