Question

In the figure, p || q.

Answer 1

M<1=m<5= corresponding 
m<2=m<6= corresponding
m<3=m<6= alternate interior
m<4=m<5= alternate interior
m<1=m<8= alternate exterior
m<2=m<7= alternate exterior
m<1=m<4= vertical
m<5=m<8= vertical
m<2=m<3= vertical
m<6=m<7= vertical

Answer 2

Answer:

Vertical angles : Opposite angles made by two intersecting lines.

Corresponding angles : which occupy the same relative position at each intersection where a straight line crosses two others.

Alternate interior angles : when a transversal passes through two line then the angles that are formed on opposite sides of the transversal and inside the two lines.

Alternate exterior angles : angles on the outer side of each of those two lines but on opposite sides of the transversal.

Here, line k passes through the lines p and q,

Thus, by the above explanation,

Vertical pairs are, angle 1 and angle 4, angle 2 and 3, angle 5 and angle 8,  angle 6 and 7,

Corresponding pairs,

angle 2 and angle 6, angle 1 and angle 5, angle 4 and angle 8, angle 3 and angle 7,

Alternate interior angles pair,

angle 4 and angle 5, angle 6 and angle 3,

Alternate exterior angles pair,

angle 2 and angle 8, angle 1 and angle 7,

Vertical angles are always equal in measure,

Now, the p and q are parallel lines,

So, the corresponding angles will be congruent as well as alternative interior or exterior will be congruent.

Therefore, the required pair,

Corresponding pairs :

m∠1=m∠5

m∠2=m∠6

Alternative interior pairs :

m∠3=m∠6

m∠4=m∠5,

Alternate exterior pairs :

m∠1=m∠8

m∠2=m∠7

Vertical pairs :

m∠1=m∠4

m∠5=m∠8

m∠2=m∠3

m∠6=m∠7