O is the Center of the circle. STU is a tangent at T .Chord BC =Chord CT;ATC=105 and CTU= 40
Calculate the size of B1+B2
We can start by using the fact that STU is a tangent at T to show that angles TBC and TUC are equal.
Since BC = CT, we can also deduce that angles BTC and BCT are equal.
Using these two facts and the fact that the angles of a triangle add up to 180 degrees, we can set up an equation:
BTC + BCT + TBC + TUC + ATC + CTU = 180
Substituting in the given values:
BTC + BCT + TBC + 40 + 105 + CTB = 180
Simplifying:
2(BTC + BCT + TBC) = 35
Dividing by 2:
BTC + BCT + TBC = 17.5
Now, notice that angles B1 and B2 are vertical angles and therefore equal.
We can also use the fact that angles TBC and CTU are equal (because they both equal angle TUC) to show that angles BCT and UCT are equal (because they both equal angle TCU).
Therefore, angles BCT and UCT add up to 40 degrees.
Using this information and the fact that angles of a triangle add up to 180 degrees, we can set up another equation:
BCT + UCT + BCU = 180
Substituting in the known values:
BCT + 40 + BCU = 180
Simplifying:
BCT + BCU = 140
But we also know from earlier that BCT + TBC + BTC = 17.5.
Substituting in BCT + TBC for BTC + BCT:
BCT + TBC + BCU = 17.5 + 140
Simplifying:
B1 + B2 = 157.5
Therefore, the size of B1 + B2 is 157.5 degrees.