Question

In the given figure, line $m\parallel n$. What is the value of $\angle 4$ if twice $\angle 2$ = $\angle 1$ ?

• A. ${60}^{\circ }$
• B. ${100}^{\circ }$
• C. ${120}^{\circ }$
• D. ${160}^{\circ }$

Answer 1

The correct option is C ${120}^{\circ }$

Let $\angle 2$ = $x^{\circ }$
Hence $\angle 1$ = $2x^{\circ }$
$\angle 2$ + $\angle 1$ = ${180}^{\circ }$ [Linear Pair]
$x^{\circ }$ + $2x^{\circ }$ = ${180}^{\circ }$
$3x^{\circ }$ = ${180}^{\circ }$
$x^{\circ }$ = ${60}^{\circ }$
$\angle 1$ = $\angle 4$ [Vertically Opposite Angles]
Hence,
$\angle 1$ = $\angle 4$ = $2x^{\circ }$ = $2\times {60}^{\circ }$ = ${120}^{\circ }$