Answer: k = 10
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Work Shown:
Use the remote interior angle theorem.
The interior angles (4k+5) and (6k+10) add to the exterior angle 115. Note the interior angles are not adjacent to the exterior angle. This is where the "remote" aspect comes in.
So,
(4k+5) + (6k+10) = 115
10k + 15 = 115
10k = 115 - 15
10k = 100
k = 100/10
k = 10
We can stop here.
If you want to keep going, then,
4k+5 = 4*10+5 = 45
6k+10 = 6*10+10 = 70
Note how 45+70 = 115 to help confirm our answer.
