In the figure, 0 is the centre of the circle ABC, < CED = 30o, < EDA = 40o. What is the size of < ABC?
A.
70o
B.
110o
C.
130o
D.
125o
E.
145o
Correct answer is D
If < CED = 30º, and < EDA = 40º then
<EOD = 180-(30-40) (angles in a triangle sum to 180) → 110º
<AOC = <EOD = 110º
At centre O: 360 - 110 = 250º
The angle subtended by an arc of a circle at its center is twice the angle it subtends anywhere on the circle's circumference.
250 * \(\frac{1}{2}\) → 125º
<ABC = 125º