Question

what is the value of v?

Explanation:

Step1: Apply 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, \(v + 41=(v + 9)+(2v-26)\).

Step2: Simplify the equation

Expand the right - hand side: \(v + 41=v + 9+2v-26\).
Combine like terms on the right - hand side: \(v + 41=3v-17\).

Step3: Solve for \(v\)

Subtract \(v\) from both sides: \(41 = 2v-17\).
Add \(17\) to both sides: \(2v=41 + 17\), so \(2v=58\).
Divide both sides by \(2\): \(v = 29\).

Answer:

\(29\)