Question

o is the circumcenter of triangle ABC, if angle BAC 85 degree and BCA 55 degree then the value of aoc is what??​

Answer 1

In a triangle ABC if o is the circumcenter then o will be the centre of the circle outsiding the triangle

so we can use the angle in semicircle formula

which is if you draw the triangle surrounded by a circle you will see that angle ABC and angle AOC are angles in a semicirle and angles in a circle

so the theory is that is one angle is in the semicircle and the other angle is in till the end circumference of the circle , then the angle in the semicircle is twice the value of angle in the circle and ends at the circumference

Hence,

2 Angle ABC = x Angle AOC

2x [ 180°-(Angle ACB + Angle BAC)]= Angle AOC

2x [ 180°-(85 + 55)] = AOC

2x [180°-130]=AOC

2 x 50°=AOC

Angle AOC = 100°