Question

what is the value of v? 30° 7v - 27° 6v + 24° v =

Explanation:

Step1: Apply 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, \(6v + 24=(7v - 27)+30\).

Step2: Simplify the equation

Simplify the right - hand side of the equation: \((7v - 27)+30=7v+(-27 + 30)=7v + 3\). The equation becomes \(6v+24 = 7v+3\).

Step3: Solve for \(v\)

Subtract \(6v\) from both sides: \(6v+24-6v=7v + 3-6v\). This gives \(24=v + 3\). Then subtract 3 from both sides: \(v=24 - 3\).

Answer:

\(v = 21\)