Question

In the adjoining figure line m II line n and line I is a transversal. If $\angle b=(x+15{)}^o$ and $\angle e=(2x+15{)}^o.$ find the value of x.

• A. ${100}^o$
• B. ${50}^o$
• C.
  ${70}^o$
• D. ${90}^o$

Answer 1

The correct option is B ${50}^o$

$(x+15{)}^o+(2x+15{)}^o={180}^o$
$\angle b\cong \angle f...$ (corresponding angles) $\therefore m\angle f=m\angle b=(x+15{)}^o$
$m\angle f+m\angle e={180}^o$ ... (Angles in linear pair)
substituting values in the equation,
$x+15+2x+15={180}^o\therefore 3x+30={180}^o$
$\therefore 3x={180}^o-{30}^o={150}^o$ ..... (subtracting 30 from both sides)
$x=\frac{{150}^o}{3}$ ....... (dividing both sides by 3)
$\therefore x={50}^o$