Question

The diagram below shows AABD with ray AC. BEI AD, and*EBD = 4CBD. If mxABE = 52, what is m&D? (4 pts]

Answer 1

According to the graph, angles ABE, EBD, and CBD are supplementary, using the theorem, we have

`\begin{gathered} m\angle ABE+m\angle EBD+m\angle CBD=180 \\ 52+2(m\angle EBD)=180 \\ 2(m\angle EBD)=180-52 \\ m\angle EBD=(128)/(2)=64 \end{gathered}`

Then, we use the interior angles theorem.

`\begin{gathered} m\angle EDB+m\angle EBD+m\angle D=180 \\ 90+64+m\angle D=180 \\ m\angle D=180-90-64=26 \end{gathered}`

Hence, the angle D measures 26°.