Question

In the given figure $AB$ and $AC$ are opposite rays
(i) If $x^{\circ }={32}^{\circ },$ find $\angle y$
ii) If $y={28}^{\circ },$ find $\angle x$

Answer 1

$2x$ and $3y+11$ are linear pair.

(i) $x={32}^o$

$2\left(32\right)+3y+11={180}^o$

$64+11+3y={180}^o$

$3y={180}^o-{75}^o$

$y=60-25$

$y={35}^o$

(ii) $y={28}^o$

$2x+3\left(28\right)+11={180}^o$

$2x={180}^o-84-11$

$2x={180}^o-{95}^o$

$2x={85}^o$

$x=\frac{{85}^o}{2}$.