Question

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

Answer 1

Side BC of $△$ABC has been produced to D.

Exterior $\angle ACD=\angle ABC+\angle BAC$

$\therefore {100}^o={65}^o+x^o$

$\Rightarrow x^o=({100}^o-{65}^o)={35}^o$

$\therefore \angle CAD=\angle BAC={35}^o$

In $△$ACD, we have:

$\angle CAD+\angle ACD+\angle CDA={180}^o$ (Angle sum property of triangle)

$\Rightarrow {35}^o+{100}^o+y^o={180}^o$

$\Rightarrow {135}^o+y^o={180}^o$

$\Rightarrow y^o=({180}^o-{135}^o)={45}^o$

Hence, $x={35}^o,y={45}^o$.