Question

In Figure, line $l\parallel m,\angle 1={120}^{\circ }$ and $\angle 2={100}^{\circ }$, find out $\angle 3$ and $\angle 4$.

• A. $\angle 3={80}^{\circ },\angle 4={40}^{\circ }$
• B.
  $\angle 3={80}^{\circ },\angle 4={60}^{\circ }$
• C. $\angle 3={40}^{\circ },\angle 4={80}^{\circ }$
• D. $\angle 3={60}^{\circ },\angle 4={80}^{\circ }$

Answer 1

The correct option is A $\angle 3={80}^{\circ },\angle 4={40}^{\circ }$

Given that $\angle 1={120}^{\circ }$ and $\angle 2={100}^{\circ }$
$\angle 1$ and $\angle 5$ a linear pair
$=\angle 1+\angle 5={180}^{\circ }=\angle 5={180}^{\circ }-{120}^{\circ }=\angle 5={60}^{\circ }$
Therefore, $\angle 5={60}^{\circ }$
$\angle 2$ and $\angle 6$ are corresponding angles
$=\angle 2=\angle 6={100}^{\circ }$
Therefore, $\angle 6={100}^{\circ }$
$\angle 6$ and $\angle 3$ a linear pair
$=\angle 6+\angle 3={180}^{\circ }=\angle 3={180}^{\circ }-{100}^{\circ }$
$=\angle 3={80}^{\circ }$
Therefore, $\angle 3={80}^{\circ }$
By angle sum property
$=\angle 3+\angle 5+\angle 4={180}^{\circ }$
$=\angle 4={180}^{\circ }-{80}^{\circ }-{60}^{\circ }=\angle 4={40}^{\circ }$
Therefore, $\angle 4={40}^{\circ }$