Isosceles triangle has and a vertex angle of . is a circle that circumscribes , and is the center of . What is the measure (in degrees) of ?
This problem is posed by Austin C.
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If you draw it correctly,
you can notice that B O cuts ∠ A B C right in the center.
So now, there will be new two angles that measure the same,
∠ A B O = ∠ C B O = 1 6 ∘ .
Since B O and C O are R ,
we can respectively say that B O = C O ,
so we get new isosceles triangle, B C O .
We now that base angles of isosceles measure the same.
That means ∠ C B O = ∠ B C O = 1 6 ∘ .
Sum of all angles of triangle will always 1 8 0 ∘ ,
then we put some of our math:
∠ B C O + ∠ C B O + ∠ B O C = 1 8 0 ∘
1 6 ∘ + 1 6 ∘ + ∠ B O C = 1 8 0 ∘
3 2 ∘ + ∠ B O C = 1 8 0 ∘
∠ B O C = 1 8 0 ∘ − 3 2 ∘
∠ B O C = 1 4 8 ∘