Question

Please help!!! I will vote BRAINLIEST What is the value of k?

Answer 1

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.