Question

1. what is the sum of a, b, c, d, and e?

Explanation:

Step1: Relate angles to arcs

Each inscribed angle ($a, b, c, d, e$) is half the measure of its intercepted arc. So:
$a=\frac{1}{2}A$, $b=\frac{1}{2}B$, $c=\frac{1}{2}C$, $d=\frac{1}{2}D$, $e=\frac{1}{2}E$, where $A,B,C,D,E$ are the intercepted arcs.

Step2: Sum the arcs

The total circumference of a circle is $360^\circ$, so:
$A+B+C+D+E=360^\circ$

Step3: Sum the angles

Substitute the angle expressions into the sum:
$a+b+c+d+e=\frac{1}{2}(A+B+C+D+E)$
Substitute the total arc measure:
$a+b+c+d+e=\frac{1}{2}(360^\circ)$

Answer:

$180^\circ$