Question

if the measure of a central angle is 120 degree find the measure of corresponding minor arc .
answer is 120 degree but how give me the full explanation​

Answer 1

if the measure of a central angle is 120 degree find the measure of corresponding minor arc .

answer is 120 degree but how give me the full explanation​

• The explanation for the answer is in accordance with the figure provided.
• Given,
• the measure of a central angle is 120 degree
• ⇒ ∠AOC = 120°
• ∴ ∠ABC =   ∠AOC / 2 = 120°/2 = 60°
• (the angle subtended by an arc in the centre is double the angle subtended by an arc on the remaining side of the circle)
• we have property of arc that,
• ∠ = 1/2 (m arc )
• (the arc subtended by the equal chords of the same circle is half the value of angle opposite to the arc made by the equal chords)
• ∠ABC = 1/2 (m arc ADC)
• 60° = 1/2 (m arc ADC)
• (m arc ADC) = 120°