Question

what is the value of v? 6v = 10v - 25 v + 17

Explanation:

Step1: Use the exterior angle theorem

The exterior angle theorem states that the measure of an exterior angle of a triangle is equal to the sum of the measures of the two non - adjacent interior angles.
So, \(10v - 25=6v+(v + 17)\)

Step2: Simplify the right - hand side

\(10v-25 = 6v+v + 17\)
\(10v-25=7v + 17\)

Step3: Isolate the variable \(v\)

Subtract \(7v\) from both sides: \(10v-7v-25=7v-7v + 17\)
\(3v-25 = 17\)
Add \(25\) to both sides: \(3v-25 + 25=17 + 25\)
\(3v=42\)
Divide both sides by \(3\): \(v=\frac{42}{3}\)

Answer:

\(v = 14\)