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:

a) Vertex of ∠2

The vertex of an angle is the common endpoint of its sides. For ∠2, the common endpoint is \( T \).

b) Sides of ∠4

The sides of an angle are the two rays that form the angle. For ∠4, the rays are \( TW \) and \( TZ \).

c) Another name for ∠3

An angle can be named using three points: the vertex and a point on each side. For ∠3, another name is \( \angle UTZ \).

d) Another name for ∠1

Using the three - point naming convention, another name for ∠1 is \( \angle XTY \).

e) Classify ∠YTW

\( \angle YTW=\angle5 = 90^{\circ}\), so it is a right angle.

f) Classify ∠YTU

\(\angle YTU=\angle5+\angle4+\angle3\). Since \(\angle5 = 90^{\circ}\) and \(\angle4+\angle3>0^{\circ}\), \(\angle YTU>90^{\circ}\) and \(\angle YTU < 180^{\circ}\), so it is an obtuse angle.

g) Classify ∠XTU

\(\angle XTU=\angle2+\angle3\). If \(\angle2+\angle3<90^{\circ}\), it is an acute angle.

h) Classify ∠WTX

\(\angle WTX=\angle4+\angle5+\angle1\). \(\angle4+\angle5+\angle1 = 180^{\circ}\), so it is a straight angle.

i) Name two perpendicular lines

Perpendicular lines form a right angle (\(90^{\circ}\)). \( TY\) and \( TW\) (since \(\angle YTW = 90^{\circ}\))

j) Name an angle bisector

If \(\angle2=\angle3\), then \( TZ\) is the angle bisector of \(\angle XTU\) (assuming \(\angle2=\angle3\) from the angle - marking in the diagram - like equal non - right angle markings)

Answer:

a) \( T\)
b) \( TW\) and \( TZ\)
c) \( \angle UTZ\)
d) \( \angle XTY\)
e) Right angle
f) Obtuse angle
g) Acute angle
h) Straight angle
i) \( TY\) and \( TW\)
j) \( TZ\) (assuming \(\angle2=\angle3\))