Question

The measures of two vertical angles are $(\sqrt{4x^2}-30{)}^o$ and $(\frac{x^2}{x}+10{)}^o$.
Determine the value of $x$.

• A. $10$
• B. $20$
• C. $30$
• D. $40$

Answer 1

The correct option is D $40$

$\underset{–}{\text{Given:}}$ Measures of two vertical angles are $(\sqrt{4x^2}-30{)}^o$ and $(\frac{x^2}{x}+10{)}^o$

$(\sqrt{4x^2}-30{)}^o=(2x-30{)}^o\Rightarrow (\frac{x^2}{x}+10{)}^o=(x+10{)}^o$

$\text{Vertical Angles Theorem}$ states that vertical angles are always congruent(equal in measure).

$\therefore$ $2x-30=x+10$
Adding $30$ on both sides,
$\Rightarrow$ $2x-30+30=x+10+30$
$\Rightarrow$ $2x=x+40$
Subtracting $x$ from both sides,
$\Rightarrow$ $2x-x=x+40-x$
$\Rightarrow$ $x=40$

So, option(d.) is correct.