Question

what is the value of ( v )?
triangle with angles ( v-19^circ ), ( v+40^circ ), ( v-5^circ )
( v = ) ( ^circ )

Explanation:

Step1: Use exterior angle theorem

The exterior angle of a triangle is equal to the sum of the two non - adjacent interior angles. So, $v + 40=(v - 19)+(v - 5)$

Step2: Simplify the right - hand side

Simplify $(v - 19)+(v - 5)$: $v-19 + v-5=2v-24$
So the equation becomes $v + 40=2v-24$

Step3: Solve for v

Subtract v from both sides: $40=2v - v-24$
Simplify: $40=v - 24$
Add 24 to both sides: $v=40 + 24$
$v = 64$

Answer:

$64$