Question

Help11-16please i dont understand

Answer 1

Answer:

  see attached

Step-by-step explanation:

There are many vocabulary words and theorems associated with angles where a transversal crosses parallel lines. These are needed for the "explain your reasoning" part of the question.

Where 2 lines cross

Where one line crosses another, the angles formed are either "adjacent" (share a side and vertex), or "vertical" (share only a vertex, formed from opposite rays). In Figure 11, x° and 67° are "adjacent" angles. In Figure 12, y° and 109° are "vertical" angles.

The adjacent angles are also called a "linear pair", and their total is 180°. They are supplementary.

The vertical angles are congruent.

Where a transversal crosses parallel lines

Two sets of four angles are formed when a transversal crosses parallel lines. The relations between angles of one of those sets and angles of the other of those sets are described using several different terms:

"Alternate" angles are on opposite sides of the transversal. "Consecutive" or "same-side" angles are on the same side of the transversal. "Exterior" angles are outside the parallel lines. "Interior" angles are between the parallel lines. "Corresponding" angles are in the same relation to the point of intersection.

Alternate exterior angles (congruent): Fig. 11, x° and y°.

Alternate interior angles (congruent): Fig. 13, y° and the one marked with the right angle symbol.

Consecutive interior angles (supplementary): Fig. 12, x° and 109°; Fig. 14, x° and y°.

Consecutive exterior angles (supplementary): none shown in these figures.

Corresponding angles (congruent): Fig 14, x° and 65°; Fig. 16, x° and 130°.

The upshot of all of these relations is this:

• all acute angles are congruent
• all obtuse angles are congruent
• obtuse angles are supplementary to acute angles
• If any angle is a right angle, all of them are.

Application

The attached table shows the values of x° and y° in the various figures. For the purpose here, we simply identified the angles as acute or obtuse, and matched values accordingly. The explanation can get as elaborate as you like. For example, ...

  11. x° and y° are alternate exterior angles, so congruent. x° and 67° are a linear pair, so x° = 180° -67° = 113°.

  12. x° and 109° are consecutive interior angles, so supplementary. x° = 180° -109° = 71°. y° and 109° are vertical angles, so congruent.