Question

what is the value of v? write your answer as an integer or as a decimal rounded to the nearest tenth.

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, $(v + 40)+(v + 60)=63v+19$.

Step2: Simplify the left - hand side

Combine like terms on the left - hand side: $v + 40+v + 60=2v+100$. So, the equation becomes $2v + 100=63v+19$.

Step3: Isolate the variable terms

Subtract $2v$ from both sides: $100=63v - 2v+19$, which simplifies to $100 = 61v+19$.

Step4: Solve for $v$

Subtract 19 from both sides: $100−19 = 61v$, so $81 = 61v$. Then, divide both sides by 61: $v=\frac{81}{61}\approx1.3$.

Answer:

$1.3$