Question

example 4
a) name the vertex of ∠2.
b) name the sides of ∠4.
c) write another name for ∠3.
d) write another name for ∠1.
e) classify ∠ytw.
f) classify ∠ytu.
g) classify ∠xtu.
h) classify ∠wtx.
i) name two perpendicular lines.
j) name an angle bisector.

Explanation:

Step1: Identify vertex

The vertex of an angle is the common - point of the two rays forming the angle. For ∠2, the vertex is point T.

Step2: Identify sides

The sides of an angle are the two rays that meet at the vertex. For ∠4, the sides are rays TZ and TW.

Step3: Rename angles

An angle can be named in different ways. ∠1 can also be named ∠XTY. ∠3 can also be named ∠UTZ.

Step4: Classify angles

• ∠YTW is a right - angle (marked with a square symbol).
• ∠YTU is an obtuse angle (it is greater than 90° but less than 180°).
• ∠XTU is an acute angle (it is less than 90°).
• ∠WTX is a straight angle (it measures 180°).

Step5: Identify perpendicular lines

Perpendicular lines intersect at a right - angle. Lines WY and XU are perpendicular.

Step6: Identify angle bisector

An angle bisector divides an angle into two equal parts. If we assume that a line divides an angle into two congruent angles, for example, if a line divides ∠WTX into two equal parts, it would be an angle bisector. But from the given information, if TY divides ∠WTX into two equal right - angles, TY is an angle bisector of ∠WTX.

Answer:

a) The vertex of ∠2 is T.
b) The sides of ∠4 are rays TZ and TW.
c) Another name for ∠3 is ∠UTZ.
d) Another name for ∠1 is ∠XTY.
e) ∠YTW is a right - angle.
f) ∠YTU is an obtuse angle.
g) ∠XTU is an acute angle.
h) ∠WTX is a straight angle.
i) Two perpendicular lines are WY and XU.
j) An angle bisector is TY (assuming it bisects ∠WTX).