quadrilateral abcd is inscribed in this circle.

what is the measure of ∠a ?

enter your answer in the box.

The measure of ∠A is 106 degrees

To get the measure of A, we will use the theorem;

From the given diagram, ∠A + ∠C = 180

∠A + ∠C = 180

∠A + 74 = 180

∠A = 180 - 74

∠A = 106 degrees

Hence the measure of ∠A is 106 degrees

Learn more on cyclic quadrilateral here: link

not to bore you to death with the "inscribed quadrilateral conjecture", but you can search for that in google, and I can even include a quick proof of it

in short what "inscribed quadrilateral conjecture" means, opposite angles, in an inscribed quadrilateral in a circle, are "supplementary angles"

meaning D + B = 180   and A + C = 180

the answer to the expression is 83

so, converting firstly the mixed fractions to improper fractions and then "adding".