Answer:
a = b = c = 45°
Step-by-step explanation:
[tex]In\: \triangle BDC, \\\\
BD = CD.... (given) \\\\
\therefore m\angle DBC =m\angle DCB\\(By\: isosceles \:\triangle\: property) \\
\therefore a\degree = b\degree.... (1)\\\\
m\angle BDC= 90\degree \\\\
\because m\angle BDC + a\degree + b\degree=180\degree \\\\
90\degree+ a\degree + a\degree=180\degree\\ [from \: equation \: (1)]\\\\
2a\degree=180\degree -90\degree\\
2a\degree= 90\degree\\\\
\therefore a\degree=\frac{ 90\degree}{2} \\\\
\huge\purple {\boxed {\therefore a\degree=45\degree}} \\\\
\implies \huge\red {\boxed { b\degree=45\degree}} \\\\
In\: \triangle ABC, \\\\
AB = BC.... (given) \\\\
\therefore m\angle BAC =m\angle BCA\\(By\: isosceles \:\triangle\: property) \\
\therefore c\degree = b\degree\\\\
\because b\degree=45\degree \\\\
\implies \huge\orange {\boxed { b\degree=45\degree}} [[/tex]
