Fill in the blanks:
(i) The measure of a straight angle is __________
(ii) The measure of a complete angle is __________
(iii) An angle lying between __________ and __________ is a reflex angle.
(iv) An angle lying between __________ and __________ is an obtuse angle.
(v) If two rays with a common end point form an angle, then their common end point is called the __________ of the angle.
Answer
(i) 180°. A straight angle is formed when the two arms of the angle lie in opposite directions along the same straight line. Half of a complete rotation is × 360° = 180°.
(ii) 360°. A complete angle is formed when a ray rotates about its end point and comes back to its initial position, that is, it makes one full rotation. Such a rotation measures 360°.
(iii) 180° and 360°. An angle is called a reflex angle when it is bigger than a straight angle but smaller than a complete angle, so its measure lies between 180° and 360°.
(iv) 90° and 180°. An angle is called an obtuse angle when it is bigger than a right angle but smaller than a straight angle, so its measure lies between 90° and 180°.
(v) vertex. The two rays forming the angle are called its arms or sides, and the common end point at which the two arms meet is called the vertex of the angle.
Write (T) for true and (F) for false for each of the statements given below:
(i) An angle measuring 180° is called a straight angle. __________
(ii) An angle measuring 360° is called a complete angle. __________
(iii) An angle measuring 180° is an obtuse angle. __________
(iv) Angle lying between 0° and 180° is called an acute angle. __________
(v) of a straight angle = 120°. __________
Answer
(i) True. An angle whose measure is 180° is a straight angle.
(ii) True. An angle whose measure is 360° is a complete angle.
(iii) False. An angle measuring 180° is a straight angle; an obtuse angle lies between 90° and 180°.
(iv) False. An acute angle lies between 0° and 90°. Angles between 0° and 180° also include right and obtuse angles.
(v) True. of a straight angle = × 180° = 120°.