the diagram shows a convex polygon.\nwhat is the value of z?\n$z = \\square^\\circ$

Explanation:

Step1: Find total interior angle sum

For a 5-sided polygon, sum = $(5-2)\times180^\circ = 540^\circ$

Step2: Sum all given angles

$109^\circ + 137^\circ + 5z + 10z + 6z = 246^\circ + 21z$

Step3: Set equal to total sum

$246 + 21z = 540$

Step4: Solve for z

$21z = 540 - 246 = 294$ $z = \frac{294}{21} = 14$

Answer:

$14$