Question

what is the value of b? b =

Explanation:

Step1: Use the exterior angle theorem

The exterior angle theorem states that an exterior angle of a triangle is equal to the sum of the two non - adjacent interior angles.
So, \(b + 20=(v - 11)+v\) and \(b + 20+(v + 30)=180\) (linear pair). But from the exterior angle theorem \(b + 20=2v-11\), and from the linear pair \(b+v=130\) (since \(b + 20+v + 30 = 180\Rightarrow b+v=130\Rightarrow v = 130 - b\)).
Substitute \(v = 130 - b\) into \(b + 20=2v-11\).

Step2: Substitute and solve for \(b\)

Substitute \(v = 130 - b\) into \(b + 20=2v-11\):

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Answer:

\(57\)