Question

what is the value of v? v + 49° 3v - 47° 2v - 16° v = °

Explanation:

Step1: Use the exterior angle theorem

The exterior angle of a triangle is equal to the sum of the two non - adjacent interior angles. So, \(v + 49=(2v - 16)+(3v - 47)\).

Step2: Simplify the right - hand side

\((2v - 16)+(3v - 47)=2v+3v-16 - 47=5v-63\). The equation becomes \(v + 49=5v-63\).

Step3: Solve for \(v\)

Subtract \(v\) from both sides: \(49 = 4v-63\). Add 63 to both sides: \(49+63 = 4v\), so \(112 = 4v\). Divide both sides by 4: \(v=\frac{112}{4}=28\).

Answer:

\(28\)