Answer:
a) Measure of A = 22.5 degrees
b) Measures for ABE and AEB: 78.75 and 78.75 degrees
c) Measures for CBE and DEB: 101.25 and 101.25 degrees
d) Measures for C and D: 78.75 and 78.75 degrees
Step-by-step explanation:
For a), notice that there are 16 sectors. Use the fact that 360 degrees is a circle, so the answer for a) is 360/16 or 90/4 or 22.5.
For b), we use the fact that AB is BE so angle ABE and AEB are the same, and since we already found out the measure of A, we can find them both by calculating 180-22.5 over 2 or 157.5/2 or 78.75 degrees for both ABE and AEB.
For c), we can just subtract what we got from ABE and AEB from 180, to get 180 - 78.75 or 101.25 as the angle measure for CBE and DEB.
For d), we just need the measure of C and D, which is the same of B and E, because ABE is similar to ACD. Or, you can use the fact that ACD is isosceles to get the same answer, 78.75 degrees.
