Question

Consider the figure:

If $\angle 1={60}^{\circ },\angle 2={70}^{\circ },and\angle x=\angle \frac{y}{2}$,
then find the value of $\angle y.$

• A. 180
• B. ${96.66}^{\circ }$
  
• C. ${76.66}^{\circ }$
  
• D. ${66.66}^{\circ }$
  

Answer 1

The correct option is A 180

$\angle$ 1 +$\angle$2+ $\angle$ACB = ${180}^{\circ }$..........................................[Property of a straight line]
$\therefore$ ${60}^{\circ }$+ ${70}^{\circ }$+$\angle$ACB = ${180}^{\circ }$
$\Rightarrow$ $\angle$ACB = ${180}^{\circ }$ - [${60}^{\circ }$ + ${70}^{\circ }$]
$\Rightarrow$ $\angle$ACB = ${180}^{\circ }$ - [${130}^{\circ }$]
$\Rightarrow$ $\angle$ACB =${50}^{\circ }$

According to the question :
$\angle$x=$\angle$$\frac{y}{2}$ .........................................................................[Given] (equation -1)

According to the angle sum property of the triangle

$\Rightarrow$$\angle$x + $\angle$y + $\angle$ACB = ${180}^{\circ }$
$\Rightarrow$ $\angle$$\frac{y}{2}$ + $\angle$y + ${50}^{\circ }$ = ${180}^{\circ }$
$\Rightarrow$ $\angle$$\frac{3y}{2}$ = ${180}^{\circ }$ - ${50}^{\circ }$
$\Rightarrow$ $\angle$$\frac{3y}{2}$ = ${130}^{\circ }$
$\Rightarrow$ $\angle$$\frac{y}{2}$ =$\frac{\left({130}^{\circ }\right)}{3}$
$\Rightarrow$ $\angle$y = $\frac{\left({130}^{\circ }\right)}{3}\times 2$ = ${86.66}^{\circ }$


$\therefore$ $\angle$y = ${86.66}^{\circ }$