Question

what are 4 statements about angles we can use to find other angle measures?
lines k and l are parallel, and the measure of angle abc is 19°.
line fg is parallel to line hj and cut by transversal m. find each angle measure:

Explanation:

Step1: Vertical - angles are equal

Vertical angles formed by two intersecting lines are congruent. For example, if two lines intersect, the opposite angles are equal in measure.

Step2: Corresponding - angles are equal

When two parallel lines are cut by a transversal, corresponding angles have the same measure. In the second diagram, if $FG\parallel HJ$ and $m$ is the transversal, the angle corresponding to the $45^{\circ}$ angle will also be $45^{\circ}$.

Step3: Alternate - interior angles are equal

For two parallel lines cut by a transversal, alternate - interior angles are congruent. In the first diagram with parallel lines $k$ and $l$ and transversal, the alternate - interior angles will have the same measure.

Step4: Supplementary angles add to 180°

Adjacent angles that form a straight - line (linear pair) or two angles whose sum is $180^{\circ}$ are supplementary. For example, in the second diagram, $a + b=180^{\circ}$.

Answer:

1. Vertical angles are equal.
2. Corresponding angles are equal when lines are parallel.
3. Alternate - interior angles are equal when lines are parallel.
4. Supplementary angles add up to 180°.