Question

I want pictures of how you did it on paper! please please please help me

Answer 1

a) The value of k in the first diagram is 10

b) The value of k in the second diagram is 7.5

Calculating angles

From the question, we are to determine the value of k in the given diagrams

a) The diagram shows two parallel lines and a transversal.

NOTE: The interior angles on the same side of the transversal are supplementary

Then, we can write that

5k + 20 + 7k + 40 = 180°

Now, solve for k

5k + 20 + 7k + 40 = 180°

12k + 60 = 180

12k = 180 - 60

12k = 120

k = 120/12

k = 10

Hence, the value of k in the first diagram is 10

b) By the exterior angle theorem, we can write that

12k + 10 + 40 = 8k + 80

NOTE: The exterior angle theorem states that the measure of an exterior angle is equal to the sum of the two opposite interior angles

Now, solve for k in

12k + 10 + 40 = 8k + 80

First, collect like terms

12k - 8k = 80 - 10 - 40

4k = 30

k = 30/4

k = 7.5

Hence, the value of k in the second diagram is 7.5

Learn more on Calculating angles here: brainly.com/question/21369105

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