Question

If x = 20 and y = 30 in the figure above, what is the value of z ?

• A. 60
• B. 70
• C. 80
• D. 90
• E. 100

Answer 1

The correct option is B 70

Given, $x$ $=$ $20$ and $y$ $=$ $30$

In the given Quadrilateral, $x,$ $x,$ $y$ are the measures of the three angles and let ${}^{\prime }{t}^{\prime }$ be the fourth unknown angle.

Sum of the interior angles of the quadrilateral $=$ $360$

$\Rightarrow x$ $+$ $x$ $+$ $y$ $+$ $t$ $=$ $360$

$\Rightarrow 20$ $+$ $20$ $+$ $30$ $+$ $t$ $=$ $360$

$\Rightarrow t$ $+$ $70$ $=$ $360$

$\Rightarrow t$ $=$ $360$ $-$ $70$

$\Rightarrow t$ $=$ $290$

To find ${}^{\prime }{z}^{\prime }$,

Sum of angles in one turn $=$ $360$

Here, $t$ $+$ $z$ $=$ $360$

$\Rightarrow z$ $+$ $290$ $=$ $360$

$\Rightarrow z$ $=$ $360$ $-$ $290$

$\Rightarrow z$ $=$ $70$

Therefore, the value of ${}^{\prime }{z}^{\prime }$ is ${}^{\prime }{70}^{\prime }$.