Question

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the diagram shows a convex polygon.
what is the value of ( v )?
( 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:

\( v = 69 \)