Question

In the figure given below, ∠DBC=90° and ∠DBE is one-third of ∠ABE. What is the measure of ∠CBE?

Answer 1

112.5°

Explanation:

`m\angle DBC = 90\degree.... (given) \\</p><p>m\angle DBE = (1)/(3)m\angle ABE.... (given) \\</p><p>m\angle ABE + m\angle DBE +m\angle DBC= 180\degree\\.. (straight \: line \: \angle 's) \\</p><p></p><p>m\angle ABE + (1)/(3)m\angle ABE +90\degree= 180\degree\\</p><p>\bigg(1+ (1)/(3)\bigg) m\angle ABE = 180\degree - 90\degree \\</p><p>\bigg((3+1)/(3)\bigg) m\angle ABE = 90\degree \\</p><p>(4)/(3) m\angle ABE = 90\degree \\</p><p>m\angle ABE = 90\degree * (3)/(4)\\</p><p>m\angle ABE = (270\degree)/(4)\\</p><p>\huge\red {\boxed {m\angle ABE = 67.5\degree}} \\</p><p>\therefore m\angle DBE = (1)/(3)* 67.5\degree \\</p><p>\huge \purple {\boxed {\therefore m\angle DBE = 22.5\degree}} \\</p><p>m\angle CBE = m\angle CBD + m\angle DBE\\</p><p>\therefore m\angle CBE = 90\degree + 22.5\degree\\</p><p>\huge \orange {\boxed {\therefore m\angle CBE = 112.5\degree}}`

Answer 2

∠DBE=1/3∠ABE ---> ∠DBE/ ∠ABE=1/3---->∠DBE/(∠DBE+∠ABE)=1/1+3

∠DBE=1/4 x 90=18 ----> ∠CBE=90 + 22.5=112.5

Explanation: