Question

Find the value of x.If necessary, you may learn what the markings on a figure indicate.740ror =

Answer 1

I would re-draw the diagram and label the angles to aid your understanding

`\begin{gathered} \text{From }\Delta ABD,\text{ }\angle\text{ BAD = }\angle BDA=74^0 \\ \angle ABD=180^{0\text{ }}-\text{ }\angle\text{ BAD - }\angle\text{ BDA (Sum of angles in a }\Delta\text{ is 180)} \\ \angle ABD=180^{0\text{ }}-74^0-74^0 \\ =32^0 \end{gathered}`
`\begin{gathered} \angle ABC=90^0\text{ (Given)} \\ \angle\text{ ABD + }\angle\text{ DBC = }\angle\text{ ABC} \\ \angle DBC=90^0-32^0 \\ =58^0 \end{gathered}`
`\begin{gathered} \text{from }\Delta\text{ CBD, }\angle\text{ CDB = }\angle\text{ BCD = x} \\ \angle\text{ CDB + }\angle\text{ BCD + }\angle DBC=180^0\text{ (Sum of angles in a straight line)} \\ x+x+58^0=180^0 \\ 2x=122^0 \\ x=61^0 \end{gathered}`