1 Answer

FrancoisBaveye · Answer 1 · 2022-07-20T17:02:47+0000

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

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