Question

what is the measure of $angle b$ of the pentagon?
$square^circ$
the pentagon has the following interior angles: $angle a=92^circ$, $angle e=150^circ$, $angle d=98^circ$, $angle c=89^circ$

Explanation:

Step1: Find total interior angle sum

For an $n$-sided polygon, the sum of interior angles is $(n-2)\times180^\circ$. For a pentagon ($n=5$):
$$(5-2)\times180^\circ = 540^\circ$$

Step2: Sum known angles

Add the given angle measures:
$$92^\circ + 150^\circ + 98^\circ + 89^\circ = 429^\circ$$

Step3: Calculate $\angle B$

Subtract the sum of known angles from total sum:
$$\angle B = 540^\circ - 429^\circ$$

Answer:

$111^\circ$