Question

HELP! i don’t understand at all

Answer 1

VYW and TYW are opposite interior angles and thus have the same value of 93 deg.

Answer 2

m∠TYW = 93°

Explanation:

When naming an angle, the three letters used in the name represent specific points or vertices that define the angle. Each letter has a distinct meaning:

• First Letter (Initial Point): This represents the starting point for one of the rays or line segments that form the angle.
• Second Letter (Vertex): This represents the point where the two rays or line segments that form the angle meet.
• Third Letter (Terminal Point): This represents the terminal point, which is the endpoint for the other ray or line segment that forms the angle.

Therefore, the angle named "VYU" refers to an angle that starts at point V, has a vertex at point Y, and ends at point U. This is shown on the attached diagram in red. Given m∠VYU = 93°:

• m∠VYU = m∠6 = 93°

The angle named "TYW" refers to an angle that starts at point T, has a vertex at point Y, and ends at point W. This is shown on the attached diagram in blue.

• m∠TYW = m∠4

Assuming that lines TU and VW are straight lines, ∠6 and ∠4 are vertically opposite angles.

According to the Vertical Angles Theorem, when two straight lines intersect, the opposite vertical angles are congruent.

Therefore, ∠4 ≅ ∠6, so:

• m∠TYW = m∠VYU

As m∠VYU = 93°, then m∠TYW = 93°.