Question 15 Marks
In the given figure, l || m and t is a transversal. If $\angle 1=55^{\circ}$, find $\angle 2, \angle 3, \angle 4, \angle 5, \angle 6, \angle 7$ and $\angle 8$.
Answer
View full question & answer→Since l || m and $\angle 1=55^{\circ}$
So, $\angle 3=\angle 1=55^{\circ}$ (Vertically opposite angles)
and $\angle 1+\angle 2=180^{\circ}$ (Linear pair)
or, $\angle 2=180^{\circ}-\angle 1=180^{\circ}-55^{\circ}=125^{\circ}$
Also, $\angle 5=\angle 3=55^{\circ}$ (Alternate interior angles)
Now, $\angle 4+\angle 5=180^{\circ}$
(Interior angles on the same side of the transversal)
or $\angle 4=180^{\circ}-\angle 5=180^{\circ}-55^{\circ}=125^{\circ}$
Also, $\angle 6=\angle 2=125^{\circ}$ (Corresponding angles)
Now $\angle 5=\angle 7=55^{\circ}$ (Vertically opposite angles)
Also, $\angle 6=\angle 8=125^{\circ}$ (Vertically opposite angles)
Hence, $\angle 2=125^{\circ}, \angle 3=55^{\circ}, \angle 4=125^{\circ}, \angle 5=55^{\circ}, \angle 6=125^{\circ}, \angle 7=55^{\circ}$ and $\angle 8=125^{\circ}$.
So, $\angle 3=\angle 1=55^{\circ}$ (Vertically opposite angles)
and $\angle 1+\angle 2=180^{\circ}$ (Linear pair)
or, $\angle 2=180^{\circ}-\angle 1=180^{\circ}-55^{\circ}=125^{\circ}$
Also, $\angle 5=\angle 3=55^{\circ}$ (Alternate interior angles)
Now, $\angle 4+\angle 5=180^{\circ}$
(Interior angles on the same side of the transversal)
or $\angle 4=180^{\circ}-\angle 5=180^{\circ}-55^{\circ}=125^{\circ}$
Also, $\angle 6=\angle 2=125^{\circ}$ (Corresponding angles)
Now $\angle 5=\angle 7=55^{\circ}$ (Vertically opposite angles)
Also, $\angle 6=\angle 8=125^{\circ}$ (Vertically opposite angles)
Hence, $\angle 2=125^{\circ}, \angle 3=55^{\circ}, \angle 4=125^{\circ}, \angle 5=55^{\circ}, \angle 6=125^{\circ}, \angle 7=55^{\circ}$ and $\angle 8=125^{\circ}$.
