Question

what is the value of v?
there is a triangle with two angles labeled as ( v - 46^circ ) and ( v - 20^circ ), and an exterior angle at the vertex opposite to these two angles labeled as ( v + 39^circ ). find the value of ( v ).
( v = square^circ )

Explanation:

Step1: Use exterior angle theorem

The exterior angle of a triangle equals the sum of the two non-adjacent interior angles. So:
$v + 39^\circ = (v - 20^\circ) + (v - 46^\circ)$

Step2: Simplify right-hand side

Combine like terms on the right:
$v + 39^\circ = 2v - 66^\circ$

Step3: Isolate variable $v$

Subtract $v$ from both sides, then add $66^\circ$ to both sides:
$39^\circ + 66^\circ = 2v - v$

Answer:

$105^\circ$