Answer:
See explanation
Step-by-step explanation:
Q1-5.
1. Plane parallel to WXT is ZYU.
2. Segments parallel to [tex]\overline {VU}[/tex] are [tex]\overline {ZY}, \overline {WX}[/tex] and [tex]\overline {ST}[/tex]
3. Segments parallel to [tex]\overline {SW}[/tex] are [tex]\overline {VZ}, \overline {YU}[/tex] and [tex]\overline {XT}[/tex]
4. Segments skew to [tex]\overline {}[/tex][tex]\overline {XY}[/tex] are [tex]\overline {SV}[/tex] and [tex]\overline {VZ}[/tex] (not lie in the same plane and not parallel)
5. Segments skew to [tex]\overline {}[/tex][tex]\overline {VZ}[/tex] are [tex]\overline {WX}[/tex] and [tex]\overline {XT}[/tex] (not lie in the same plane and not parallel)
Q6.
a. [tex]\angle 4[/tex] and [tex]\angle 10[/tex] are the same-side interior angles, transversal k
b. [tex]\angle 8[/tex] and [tex]\angle 11[/tex] are alternate exterior angles, transversal m
c. [tex]\angle 1[/tex] and [tex]\angle 4[/tex] do not form any pair of angles
d. [tex]\angle 2[/tex] and [tex]\angle 12[/tex] are the same-side exterior angles, transversal k
e. [tex]\angle 5[/tex] and [tex]\angle 7[/tex] are corresponding angles, transversal j
f. [tex]\angle 2[/tex] and [tex]\angle 13[/tex] are alternate interior angles, transversal l
Q7.
[tex]m\angle 1=m\angle 7=131^{\circ}[/tex] (as vertical angle with angle 7)
[tex]m\angle 2=180^{\circ}-131^{\circ}=49^{\circ}[/tex] (as supplementary angle with angle 1)
[tex]m\angle 8=49^{\circ}[/tex] (as vertical angle with angle 2)
[tex]m\angle 3=m\angle 1=131^{\circ}[/tex] (as corresponding angles when parallel lines p and q are cut by transversal r)
[tex]m\angle 4=m\angle 2=49^{\circ}[/tex] (as corresponding angles when parallel lines p and q are cut by transversal r)
[tex]m\angle 5=m\angle 7=131^{\circ}[/tex] (as corresponding angles when parallel lines p and q are cut by transversal r)
[tex]m\angle 6=m\angle 8=49^{\circ}[/tex] (as corresponding angles when parallel lines p and q are cut by transversal r)
[tex]m\angle 10=m\angle 16=88^{\circ}[/tex] (as vertical angle with angle 16)
[tex]m\angle 9=180^{\circ}-88^{\circ}=92^{\circ}[/tex] (as supplementary angle with angle 16)
[tex]m\angle 15=92^{\circ}[/tex] (as vertical angle with angle 9)
[tex]m\angle 14=m\angle 16=88^{\circ}[/tex] (as corresponding angles when parallel lines p and q are cut by transversal s)
[tex]m\angle 13=m\angle 15=92^{\circ}[/tex] (as corresponding angles when parallel lines p and q are cut by transversal s)
[tex]m\angle 12=m\angle 10=88^{\circ}[/tex] (as corresponding angles when parallel lines p and q are cut by transversal s)
[tex]m\angle 11=m\angle 9=92^{\circ}[/tex] (as corresponding angles when parallel lines p and q are cut by transversal s)
Q8.
[tex]m\angle 7=m\angle 9=105^{\circ}[/tex] (as vertical angles)
[tex]m\angle 8=180^{\circ}-105^{\circ}=75^{\circ}[/tex] (as supplementary angle with angle 9)
[tex]m\angle 10=m\angle 8=75^{\circ}[/tex] (as vertical angles)
[tex]m\angle 6=m\angle 8=75^{\circ}[/tex] (as alternate interior angles when parallel lines a and b are cut by transversal c)
[tex]m\angle 1=180^{\circ}-75^{\circ}-63^{\circ}=42^{\circ}[/tex] (by angle addition postulate)
[tex]m\angle 3=180^{\circ}-42^{\circ}-63^{\circ}=75^{\circ}[/tex] (by angle addition postulate)
[tex]m\angle 4=m\angle 1=42^{\circ}[/tex] (as vertical angles)
[tex]m\angle 5=m\angle 2=63^{\circ}[/tex] (as vertical angles)
[tex]m\angle 11=m\angle 4=42^{\circ}[/tex] (as alternate interior angles when parallel lines a and b are cut by transversal d)
[tex]m\angle 12=180^{\circ}-42^{\circ}=138^{\circ}[/tex] (as supplementary angles)
[tex]m\angle 13=m\angle 11=42^{\circ}[/tex] (as vertical angles)
[tex]m\angle 14=m\angle 12=138^{\circ}[/tex] (as vertical angles)
