Question

the diagram shows a convex polygon.
what is the value of p?
p = \boxed{\space}^\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 add up all the given exterior angles and set the sum equal to \(360^\circ\).
The exterior angles are \(p^\circ\), \((2p - 49)^\circ\), \(2p^\circ\), \((p + 25)^\circ\), and \((p - 29)^\circ\).
So the equation is: \(p+(2p - 49)+2p+(p + 25)+(p - 29)=360\)

Step2: Simplify the left - hand side of the equation

Combine like terms:
\(p+2p+2p+p+p-49 + 25-29=360\)
\((1 + 2+2 + 1+1)p+(-49 + 25-29)=360\)
\(7p+(-53)=360\)
\(7p-53 = 360\)

Step3: Solve for \(p\)

Add 53 to both sides of the equation:
\(7p-53 + 53=360 + 53\)
\(7p=413\)
Divide both sides by 7:
\(p=\frac{413}{7}=59\)

Answer:

\(p = 59^\circ\)