Answer: 51
===========================================================
Step-by-step explanation:
Your teacher shows that minor arc BD is 129 degrees. Recall that any minor arc is always less than 180 degrees.
Let's say that we had point A at the center of the circle. This would mean angle DAB is 129 degrees. This central angle subtends or cuts off minor arc BD.
Now focus entirely on quadrilateral DABC. The goal is to find the unknown angle C. The angle A was found earlier at 129 degrees. The angles B and D are 90 degrees each since tangents are perpendicular to the radius at the point of tangency.
We have this so far
- A = 129
- B = 90
- C = unknown
- D = 90
Adding all four angles of any quadrilateral will always get us 360 degrees. It's similar to how adding the angles of a triangle gets us 180 degrees. In fact, any quadrilateral can be cut into two triangles (aka the process of triangulation). So adding two triangles gets us 180+180 = 360 more or less.
--------------
Anyways, the four angles A,B,C,D must add to 360. So,
A+B+C+D = 360
129+90+C+90 = 360
C+309 = 360
C = 360-309
C = 51
--------------
As a shortcut, note how B+D = 90+90 = 180
Also note that A+C = 360-(B+D) which becomes A+C = 180
So, C = 180-A = 180-129 = 51