the diagram shows a convex polygon.\nwhat is the value of ( v )?\n( v = square^circ )

Explanation:

Step1: Recall the exterior angle sum of a polygon

The sum of the exterior angles of any convex polygon is ( 360^\circ ). So we can set up the equation by adding the given exterior angles: ( 119^\circ+(2v - 40)^\circ+(2v + 5)^\circ=360^\circ )

Step2: Simplify the left - hand side of the equation

First, combine like terms. The constant terms: ( 119-40 + 5=84 ), and the terms with ( v ): ( 2v+2v = 4v ). So the equation becomes ( 4v+84 = 360 )

Step3: Solve for ( v )

Subtract 84 from both sides of the equation: ( 4v=360 - 84=276 ) Then divide both sides by 4: ( v=\frac{276}{4} = 69 )

Answer:

( v = 69 )