Question

what does a =?and what is the measure of each angle (A,B,Y,C)

Answer 1

Remember that

In an inscribed quadrilateral, opposite angles are supplementary

so

B+Y=180 degrees

A+C=180 degrees

B+Y=180

substitute given values

(a+16)+(a-18)=180

solve for a

2a-2=180

2a=182

a=91

Find the measure of each angle

B=a+16=91+16=107 degrees

A=a+30=91+30=121 degrees

Y=a-18=91-18=73 degrees

C=180-A=180-121=59 degrees