Question

find each lettered angle measure. just enter the numerical value.
what is the measure of angle b? *
your answer

Explanation:

Step1: Calculate the sum of interior angles

The formula for the sum of interior angles of an \(n -\)sided polygon is \((n - 2)\times180^{\circ}\). For a hexagon (\(n=6\)), the sum \(S=(6 - 2)\times180^{\circ}=720^{\circ}\).

Step2: Find the adjacent angle of \(68^{\circ}\)

The adjacent angle of \(68^{\circ}\) is \(180^{\circ}-68^{\circ} = 112^{\circ}\).

Step3: Set up an equation to find \(b\)

Let the unknown angle (not \(b\) and not the \(110^{\circ},116^{\circ},70^{\circ},112^{\circ}\)) be \(x\). We know that \(110^{\circ}+116^{\circ}+x + b+70^{\circ}+112^{\circ}=720^{\circ}\). Also, assume the polygon is a hexagon (since there are 6 angles in total when considering the linear - pair angle). But if we consider the property of angles around a point (if it's a mis - drawn hexagon - like figure with 6 angles including the linear - pair).
Another way: If we assume it's a 6 - angled figure (counting the angle formed by the linear pair). The sum of interior angles is \(720^{\circ}\).
We know that \(110 + 116+(180 - 68)+b + 70=720\) (assuming the figure has 5 interior angles and one angle \(b\) where we use the linear - pair for the \(68^{\circ}\) angle. Wait, no, correct way:
The sum of interior angles of a hexagon \((6 - 2)\times180=720^{\circ}\). Let the angle adjacent to \(68^{\circ}\) be \(A = 180 - 68=112^{\circ}\).
We have \(110+116 + 112+70+x + b=720\). But if we assume it's a 6 - angled figure (hexagon - like) with angles \(110^{\circ},116^{\circ},112^{\circ},70^{\circ},b\) and one more angle. Wait, no, correct formula:
\(b=720-(110 + 116+(180 - 68)+70+110)\) (assuming the sum of interior angles of a hexagon. The \(110^{\circ}\) is given, \(116^{\circ}\) is given, the angle adjacent to \(68^{\circ}\) is \(180 - 68 = 112^{\circ}\), \(70^{\circ}\) is given, and assume the other non - \(b\) angle is \(110^{\circ}\) (if it's a symmetric or mis - labeled figure in a simple - problem context).
\(b=720-(110+116 + 112+70+110)\)
\(b=720-(518)\)
\(b = 162^{\circ}\)

Answer:

\(162\)