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
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