Question

There are four angles formed at a point say, $w,x,y,z$.

If $w=x=y$ and $z=2x$. Find the value of $w,x,y,z$.

• A. $w=x=y=$${72}^o$, $z=$${144}^o$
• B. $w=x=y=$${144}^o$, $z=$${72}^o$
• C. $w=x=y=$${60}^o$, $z=$${120}^o$
• D. $w=x=y=$${90}^o$, $z=$${180}^o$

Answer 1

The correct option is A $w=x=y=$${72}^o$, $z=$${144}^o$

Given, $x=y=w$
and $z=2x$
As we know , sum of angle at a point is ${360}^o$
$\therefore w+x+y+z={360}^o$
$x+x+x+2x={360}^o$ (As $w=y=x$ and $z=2x$)
$5x={360}^o$
$x=\frac{360}{5}$
$\therefore x=y=w={72}^o$
and $z=2\times x=2\times {72}^o={144}^o$