Question

In the given figure two parallel lines l,m are intersected by a tranversal. If $\angle 2={65}^{\circ }$ then $\angle 7$ and $\angle 6$ are

• A. ${105}^{\circ },{75}^{\circ }$
• B. ${125}^{\circ },{55}^{\circ }$
• C. ${115}^{\circ },{65}^{\circ }$
• D. ${95}^{\circ },{85}^{\circ }$

Answer 1

The correct option is C

${115}^{\circ },{65}^{\circ }$

Given,$l\parallel m$ and $\angle 2={65}^{\circ }$

$\angle 2+\angle 7={180}^{\circ }$ [ Exterior allied angles]

$\Rightarrow {65}^{\circ }+\angle 7={180}^{\circ }$

$\Rightarrow \angle 7={180}^{\circ }-{65}^{\circ }={115}^{\circ }$

$\angle 2=\angle 6$ [ Corresponding angles]

$\angle 2={65}^{\circ }$