Question

In the diagram, lines r and s are parallel to each other and perpendicular to transversal line t. Line w is a transversal to lines r and s. Use properties of special angles, formed by parallel lines, perpendicular lines and their transversals, to describe the relationship between the angles. Choose all of the situations that correctly describe the relationship between the angles. Note: Figure is not drawn to scale
s || r ; s ⊥ t ; r ⊥ t
line w is a transversal

same side interior angles
alternate interior angles
equal angles
alternate exterior angles
supplementary angles
right angles
corresponding angles
vertical angles
The angles do not share a special relationship.

Answer 1

Answer:

equal angles and vertical angles

Step-by-step explanation:

we know that

Vertical Angles are the angles opposite each other when two lines cross. They are always equal

In this problem

∠14=∠16 -----> by vertical angles

therefore

The answer is

equal angles and vertical angles

Answer 2

Answer:

Vertical angles, equal angles

Step-by-step explanation:

when a transversal passes through two lines, then,

Angles formed in the same side and inside the two lines are same side interior angles.

Angles that are formed on opposite sides of the transversal and inside the two lines are alternate interior angles.

Angles formed on opposite sides of the transversal and outside the two lines are alternate exterior angles.

Angles with the same relative position at each intersection are corresponding angles,

While, when two lines intersect each other then the opposite angles formed called vertical angles,

supplementary angles : When the sum of two angles are 180°,

Right angles : angle that has the measurement of 90°,

Equal angles : angles with the same measurement.

Now, vertical angles are always equal angles,

Also, when two parallel lines are cut by the same transversal then the pair of alternate interior angles, alternate exterior angles, corresponding angles are always equal.

Hence, by above definitions it is clear that,

∠16 and ∠14 are vertical and equal angles.