Question

(b) If m∠DBC is three times that of m∠ABE, find m∠DBC.

Answer 1

Angle DBC=3*Angle ABE

Angle DBC+Angle ABE+Angle EBD=180

Angle EBD=90

`\begin{gathered} \measuredangle DBC+\measuredangle ABE+90=180 \\ 3\cdot\measuredangle ABE+\measuredangle ABE+90=180 \\ 4\cdot\measuredangle ABE+90=180 \\ 4\cdot\measuredangle ABE=180-90 \\ 4\cdot\measuredangle ABE=90 \\ \measuredangle ABE=(90)/(4)=22.5 \end{gathered}`

Angle DBC will be

`\begin{gathered} \measuredangle DBC=3\cdot\measuredangle ABE \\ \measuredangle DBC=3\cdot(22.5) \\ \measuredangle DBC=67.5 \end{gathered}`