Question

ABCD is a rhombus with diagonals intersecting at E. If the measure of angle ABC is 3 times the measure of angle BAD, find the measure of angle EBC.

Answer 1

The opposite interior angles in a rhombus must be equivalent,

therefore:

`\begin{gathered} m\angle ABC=3m\angle BAD \\ where \\ m\angle ABC=m\angle ADC \\ m\angle BAD=m\angle DCB \\ so\colon \\ 3m\angle BAD+3m\angle BAD+m\angle BAD+m\angle BAD=180 \\ 8m\angle BAD=180 \\ m\angle BAD=(180)/(8) \\ m\angle BAD=22.5 \end{gathered}`

Hence:

`m\angle ABC=3m\angle BAD=67.5`
`\begin{gathered} m\angle EBC=(m\angle ABC)/(2) \\ m\angle EBC=(67.5)/(2) \\ m\angle EBC=33.75 \end{gathered}`