Answer:
112.5°
Step-by-step explanation:
[tex] m\angle DBC = 90\degree.... (given) \\
m\angle DBE = \frac{1}{3}m\angle ABE.... (given) \\
m\angle ABE + m\angle DBE +m\angle DBC= 180\degree\\.. (straight \: line \: \angle 's) \\
m\angle ABE + \frac{1}{3}m\angle ABE +90\degree= 180\degree\\
\bigg(1+ \frac{1}{3}\bigg) m\angle ABE = 180\degree - 90\degree \\
\bigg(\frac{3+1}{3}\bigg) m\angle ABE = 90\degree \\
\frac{4}{3} m\angle ABE = 90\degree \\
m\angle ABE = 90\degree \times \frac{3}{4}\\
m\angle ABE = \frac{270\degree}{4}\\
\huge\red {\boxed {m\angle ABE = 67.5\degree}} \\
\therefore m\angle DBE = \frac{1}{3}\times 67.5\degree \\
\huge \purple {\boxed {\therefore m\angle DBE = 22.5\degree}} \\
m\angle CBE = m\angle CBD + m\angle DBE\\
\therefore m\angle CBE = 90\degree + 22.5\degree\\
\huge \orange {\boxed {\therefore m\angle CBE = 112.5\degree}} [/tex]
