Question

In the diagram below, every pair of segments which do not intersect are parallel, and the measure of angle k is 89 degrees. What is the total number of degrees in angles s,e,q,u,o,i,a?

Answer 1

633 degrees

Explanation:

Angles i and l are each supplementary to k, so they each measure 180 degrees - 89 degrees =91 degrees. Then angle j is supplementary to each of i and l, so the measure of j is 180 degrees - 89 degrees =91 degrees, the same as k.

Thus, we've measured all the angles in the cluster of angles that share a vertex with k. Every other cluster of angles is congruent to this one, because these clusters are all formed by a single transversal of six parallel lines.

Thus,

s+e+q+u+o+i+a = 89 degrees + 91 degrees + 91 degrees + 91 degrees + 89 degrees + 91 degrees + 91 degrees

= (7 x 90 - 2 + 5) degrees

= 633 degrees

The total number of degrees is 633.

Answer 2

From the figure shown:
Given that k=89, then:
c=g=k=o=s=w=89
b=f=j=n=r=v=89
d=h=l=p=t=x=180-89=91
a=e=i=m=q=u=91
thus the sum of s,e,q,u,o,i,a will be:
s+e+q+u+o+i+a
=89+91+91+91+89+91+91
=633°

Answer: 633°