Question

the diagram shows a convex polygon. what is the value of b? b = \boxed{\circ}

Explanation:

Step1: Count polygon sides

It is a pentagon (5 sides).

Step2: Calculate total interior angles

Formula: $(n-2)\times180^\circ$. For $n=5$: $(5-2)\times180=540^\circ$.

Step3: Set up angle sum equation

Sum of angles: $2b + 2b + 2b + 106 + 116 = 540$.

Step4: Simplify and solve for b

$6b + 222 = 540$ → $6b=318$ → $b=53$.

Answer:

53