Given:
A figure in which a transversal line t intersect the two parallel lines a and b.
To find:
The measure of the numbered angles.
Solution:
If a transversal line intersect the two parallel lines, then
1. Corresponding angles are equal.
2. Alternate interior angles are equal.
3. Alternate exterior angles are equal.
Now,
[tex]m\angle 1+99^\circ=180^\circ[/tex] (Linear pair)
[tex]m\angle 1=180^\circ-99^\circ[/tex]
[tex]m\angle 1=81^\circ[/tex]
[tex]m\angle 2=99^\circ[/tex] (Vertically opposite angles)
[tex]m\angle 3=\angle 1=81^\circ[/tex] (Vertically opposite angles)
[tex]m\angle 4=99^\circ[/tex] (Corresponding angles)
[tex]m\angle 5=\angle 3=81^\circ[/tex] (Alternate interior angles)
[tex]m\angle 6=99^\circ[/tex] (Alternate exterior angles)
[tex]m\angle 7=\angle 3=81^\circ[/tex] (Corresponding angles)
Therefore, [tex]\angle 1=81^\circ, \angle 2=99^\circ,\angle 3=81^\circ, \angle 4=99^\circ,\angle 5=81^\circ, \angle 6=99^\circ,\angle 7=81^\circ[/tex].
