Are two opposite rays with common endpoint considered to have an angle? Why?
2 Answers | Add Yours
Yes. Any two rays joined with an endpoint always have, by definition, an angle between them. Two opposite rays form a straight line. The angle of a straight line is 180 degrees. To see this, imagine that one ray is tilted slightly up or down from being exactly a straight line. Then the angle between the rays would be about 179 degrees, or 181 degrees.
Even two rays joined with an endpoint and pointing in the same direction have an angle between them: it is 360 degrees (or 0 degrees).
An angle is formed by any two lines(or rays) meeting at a common point. It has a measure.They can be added . They can be subtracted.
Let AO and BO be opposite rays meeting at O.
Construction: Let a ray from CO come from C and meet at O.
Now AOB is a straifght line as two opposite rays meet at O.
But AOC is an angle, AO and CO are two rays meeting at O
BOC is another angle., for the similar reason.
But AOC+BOC = AOC. Therefore, AOC being the sum of two angles is also an angle.
Therefore, opposite rays meeting at a common point is considered to be anangle , or rather is an angle.
When the two rays AO and BO meet at O, there is an angle contained beween them AO and BO (or OA and OB)
Keeping BO fixed, O of OA fixed on O of OB ,you can move OA about O like a compass. For any position A, there is an angle between the arms AOB. Therefore, When AO comes exacctly opposite to BO, AOB becomes one sraight light line. Even then there is measure of angle berween AO and BO and it is a special angle called straight angle measuring 180degrees (or Pi radians).
Join to answer this question
Join a community of thousands of dedicated teachers and students.Join eNotes