Question

Using the information given in the adjacent figure, find the value of x and y.

Answer 1

Side BC of $△$ABC has been produced to D.
$\therefore$ Exterior angle $\angle ACD=\angle BAC+\angle ABC$
$\Rightarrow x^o={30}^o+{35}^o={65}^o$
Again, side CE of $△$DCE has produced to A.
$\therefore$ Exterior angle $\angle DEA=\angle EDC+\angle ECD$
$\Rightarrow y=45+x^o={45}^o+{65}^o={110}^o$.
Hence, $x={65}^o$ and $y={110}^o$.