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Answer:
[tex] m\angle CBD = 35\degree [/tex]
[tex] m\angle DBE = 92\degree [/tex]
Step-by-step explanation:
[tex] m\angle CBD = m\angle FBG[/tex]
(Vertical angles)
[tex] \because m\angle FBG = 35\degree [/tex]
[tex] \therefore m\angle CBD = 35\degree [/tex]
[tex] m\angle DBE +m\angle ABD= 180\degree [/tex]
(Linear pair angles)
[tex] m\angle DBE +m\angle CBD + m\angle ABC = 180\degree [/tex]
[tex] m\angle DBE + 35\degree + 53\degree = 180\degree [/tex]
[tex] m\angle DBE + 88\degree = 180\degree [/tex]
[tex]m\angle DBE = 180\degree -88\degree [/tex]
[tex] m\angle DBE = 92\degree [/tex]
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