Explanation:
6.) Linear Pairs and Vertical Angles
Linear pairs occur when two lines intersect each other at a single point (vertex). If two angles form a linear pair, then the measures of the angles add up to 180°. The following are the linear pairs formed by the intersection of two lines:
< 1 and < 2
< 2 and < 3
< 3 and < 4
< 1 and < 4
Vertical angles are two congruent angles whose sides form pairs of opposite rays. The exterior sides of two adjacent angles lie along the same line, and their angles are supplementary.
The vertical angles are:
< 1 and < 3
< 2 and < 4
7 ) Parallel and Perpendicular Lines:
Two coplanar lines that do not intersect are parallel. If a transversal intersects two lines such that the corresponding angles are congruent, then the two lines are parallel.
If two parallel lines are cut by a transversal, then the following are all congruent:
- corresponding angles
- alternate interior angles
- alternate exterior angles
- same side interior angles:
Perpendicular lines are two lines that meet to form congruent adjacent angles. In other words, if two lines are perpendicular, then they meet to form right angles.
8) Vertical Angles, Linear Pairs, Corresponding Angles:
Vertical angles:
< 1 and < 4, < 2 and < 3, < 5 and < 8, < 7 and < 6
Linear pairs:
< 1 and < 2, < 3 and < 4, < 1 and < 3, < 2 and < 4, < 5 and < 6, < 7 and < 8, < 5 and < 7, < 6 and < 8.
Corresponding angles:
< 1 and < 5, < 2 and < 6, < 4 and < 8, < 3 and < 7.
9.)
The supplement of angle m < 50° is the corresponding angle of < x. Therefore, m < x° = 180° - m < 50° = 130°