Question

7 multiple choice 6 points
what is the measure of $angle b$
$\bigcirc$ $98^circ$
$\bigcirc$ $108^circ$
$\bigcirc$ $118^circ$
$\bigcirc$ $128^circ$

Explanation:

Step1: Find total interior angle sum

The formula for the sum of interior angles of an $n$-sided polygon is $(n-2)\times180^\circ$. For a hexagon ($n=6$):
$$(6-2)\times180^\circ = 4\times180^\circ = 720^\circ$$

Step2: Identify known angles

$\angle A=170^\circ$, $\angle C=133^\circ$, $\angle D=102^\circ$, $\angle E=117^\circ$, $\angle F=90^\circ$ (right angle)

Step3: Calculate sum of known angles

$$170^\circ + 133^\circ + 102^\circ + 117^\circ + 90^\circ = 612^\circ$$

Step4: Solve for $\angle B$

Subtract known sum from total sum:
$$\angle B = 720^\circ - 612^\circ = 108^\circ$$

Answer:

108° (the second option: 108°)