Answers:
- a = 64
- b = 112
- c = 78
- d = 88
==========================================
Step-by-step explanation:
The 102 inscribed angle cuts off the arc that's composed of the 140 and 'a'.
Due to the inscribed angle theorem, we know that a+140 is exactly equal to twice that of 102.
This means,
a+140 = 2*102
a+140 = 204
a = 204-140
a = 64
-----------------
The angles 102 and c are inscribed angles opposite one another. They add to 180. This is true for any inscribed quadrilateral.
c+102 = 180
c = 180-102
c = 78
-----------------
Another useful rule is that the four angles of any quadrilateral always add to 360.
102+92+c+d = 360
102+92+78+d = 360
272+d = 360
d = 360-272
d = 88
-----------------
The inscribed angle d cuts off the arc a+b
This means 2d is the measure of a+b because of the inscribed angle theorem.
a+b = 2d
64+b = 2*88
64+b = 176
b = 176-64
b = 112