Question

Angle in a minor segment is
A. An acute angle
B. An obtuse angle
C. A right angle
D. A reflexive angle

Answer 1

Hint: In order to find the solution of this question, we should know that the segment is a portion that is formed by the chord by cutting a circle into two parts which may be equal or may not be equal. So, the angle of segment will be the angle subtended by the chord to the circumference of the circle.

Complete step-by-step answer:
In this question, we have been asked to find the type of angle formed in a minor segment. Now, we know that segment of a circle is a portion of the circle which is formed by the chord that cuts it into two parts that may be equal or not. So, the minor segment would be that portion of the circle which does not include the centre, when the chord divides the circle into two unequal parts. We can say that the minor segment would look something like the figure given below.

So, when we talk about the angle in a segment, then we talk about the angle that is formed by the chord to the circumference of the circle. Now, we know that the diameter of the circle always subtends $90{}^{\circ }$ to the circumference of the circle. We also know that if we draw an angle to a more distant point from line AB, than the nearer point, then angle at the distant point would be less than the angle at the nearer point. So, the same applies to a circle also. That is, if we shift the chord from the centre to the point where angle is subtended, then the angle will increase and if angle becomes greater than $90{}^{\circ }$, then it becomes an obtuse angle.
So, we can say that the angle in the minor segment is an obtuse angle.
Therefore, option B is the correct answer.

Note: While solving this question, we need to remember that acute angles are the angles that are less than $90{}^{\circ }$, but greater than $0{}^{\circ }$, obtuse angles are angles that are greater than $90{}^{\circ }$, but lesser than $180{}^{\circ }$, right angle is $90{}^{\circ }$ and reflexive angles are those which are greater than $180{}^{\circ }$, but lesser than $360{}^{\circ }$.