Question

In the given figure two parallel lines l,m are intersected by a tranversal. If $\angle 4={45}^{\circ }$ then $\angle 3$ and $\angle 6$ are

• A. $\angle 3={135}^{\circ }$
• B. $\angle 3={145}^{\circ }$
• C. $\angle 6={75}^{\circ }$
• D. $\angle 6={45}^{\circ }$

Answer 1

Answer: (A), (D)

The correct options are
A

$\angle 3={135}^{\circ }$

D

$\angle 6={45}^{\circ }$

Given,$l\parallel m$ and $\angle 4={45}^{\circ }$

$\angle 3+\angle 4={180}^{\circ }$ [Linear Pair]

$\Rightarrow \angle 3+{45}^{\circ }={180}^{\circ }$

$\Rightarrow \angle 3={135}^{\circ }$

Also, $\angle 4=\angle 6$ [Interior alternate angles]

$\therefore \angle 6={45}^{\circ }$