Question

In figure, $\angle POR$ and $\angle QOR$ form a linear pair. If $a-b=80$, then the values of $a$ and $b$ are

• A. $a=50$, $b=130$
• B. $a=130$, $b=50$
• C. $a=260$, $b=60$
• D. $a=60$, $b=260$

Answer 1

Answer: (B)

$a=130$, $b=50$

$\angle POR$ and $\angle QOR$ form a linear pair,
$\therefore \angle POR+\angle QOR=180$ (Linear pair axiom)
$a+b=180$ ...........(1)
But $a-b=80$ ...........(2) [Given]
Adding equations (1) and (2), we get
$2a=260$
$\therefore a=\frac{260}{2}=130$
Substituting the value of $a$ in (1), we get
$130+b=180$
$\Rightarrow b=180-130=50$