Question

if the measure of a central angle is 120° , find the measure of the corresponding minor arc and that of major arc

Answer 1

this is the figure according to your question
the central angle is 120° so angle BAC = 120°÷ 2 (because the angle subtended by an arc in the centre is double the angle made by an arc on remaining side of the circle ) so angle BAC = 60°
also we can see that ABCD is a cyclic quadrilateral and also we know that the sum of opposite angles of the cyclic quadrilateral is 180°
so,angle BDC = 60° +x = 180°
BDC= x = 180-60= 120°

Answer 2

Step-by-step explanation:

central angle = corresponding angle

so central angle =120°