Question

In the adjacent figure, find the value of $x,y,z$ and $a,b,c$.

Answer 1

Clearly, we have

$y^o={110}^o$ ($\because$ Corresponding angles)

$\Rightarrow x^o+y^o={180}^o$ (linear pair)

$\Rightarrow x^o+{110}^o={180}^o$

$\Rightarrow x^o=({180}^o-{110}^o)={70}^o$

$z^o=x^o={70}^o$ ($\because$ Corresponding angles)

$c^o={65}^o$

$a^o+c^o={180}^o$ [Linear pair]

$\Rightarrow a^o+{65}^o={180}^o$

$\Rightarrow a^o=({180}^o-{65}^o)={115}^o$

$b^o=c^o={65}^o$ [$\because$ Vertically opposite angles]

Hence, $a={115}^o,b={65}^o,c={65}^o,x={70}^o,y={110}^o,z={70}^o$