In the figure, p || q.

identify each pair of equal angles as vertical angles, corresponding angles, alternate interior angles, or alternate exterior angles.

m< 3 = m< 7:

m< 1 = m< 4:

m< 5 = m< 8:

m< 1 = m< 5:

m< 1 = m< 8:

m< 2 = m< 6:

m< 2 = m< 3:

m< 4 = m< 8:

m< 6 = m< 7:

m< 3 = m< 6:

m< 2 = m< 7:

m< 4 = m< 5:

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

9.55 degrees.

step-by-step explanation:

the given angle is

1 cycle is equal to 2π radians. so 4π will be equal to two cycles.

5.166667π-4π = 1.166667π

hence, this angle goes a little more than negative x axis.

1.166667π-π= 0.166667π

hence, the reference angle is 0.166667π radians.

1 radian = 57.2958 degrees

now, in degrees, this should be equals to 9.55 degrees.