Question

Use the figure to find the measures of the numbered angles,

Answer 1

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,

$m\angle 1+99^\circ=180^\circ$              (Linear pair)

$m\angle 1=180^\circ-99^\circ$

$m\angle 1=81^\circ$

$m\angle 2=99^\circ$                         (Vertically opposite angles)

$m\angle 3=\angle 1=81^\circ$                (Vertically opposite angles)

$m\angle 4=99^\circ$                         (Corresponding angles)

$m\angle 5=\angle 3=81^\circ$                (Alternate interior angles)

$m\angle 6=99^\circ$                         (Alternate exterior angles)

$m\angle 7=\angle 3=81^\circ$                (Corresponding angles)

Therefore, $\angle 1=81^\circ, \angle 2=99^\circ,\angle 3=81^\circ, \angle 4=99^\circ,\angle 5=81^\circ, \angle 6=99^\circ,\angle 7=81^\circ$.