Question

In the figure above, lines $l$ and $k$ intersect at point $Q$. If $m={40}^o$ and $p={25}^o$, what is the value of $x$ ?

• A. ${15}^o$
• B. ${20}^o$
• C. ${25}^o$
• D. ${40}^o$
• E. ${65}^o$

Answer 1

Answer: (A)

${15}^o$

Given, lines ${}^{\prime }{l}^{\prime }$ and ${}^{\prime }{k}^{\prime }$ intersect.

Vertically opposite angles are the angles that are opposite to each other when two lines intersect.

Vertically opposite angles are equal.

Here, ${}^{\prime }{m}^{\prime }$ and ${}^{\prime }$$\angle lQk$${}^{\prime }$ are vertically opposite angles and are equal.

$\Rightarrow m$ $=$ $\angle lQk$

$\Rightarrow m$ $=$ $p$ $+$ $x$

To find ${}^{\prime }{x}^{\prime }$, when $m$ $=$ $40$ and $p$ $=$ $25$,

$\Rightarrow x$ $=$ $m$ $-$ $p$

$\Rightarrow x$ $=$ $40$ $-$ $25$

$\Rightarrow x$ $=$ $15$

Therefore, the value of ${}^{\prime }{x}^{\prime }$ is ${}^{\prime }{15}^{\prime }$.