# Construct the following angles and verify by measuring them by a protractor:(i) 75°(ii) 105°(iii) 135°

(i) Given, to construct an angle of 75° from the initial point of a ray.

Steps of Construction:

a. Draw a ray AB of any length. b. Now as point A is the initial point as the centre, draw an arc any radius such that, the arc meets the ray AB at point C. c. With C as centre and with the same radius as before, draw another arc cutting the previous one at point D. d. Now with D as centre and with the same radius, draw an arc cutting the first arc (drawn in step ii) at point E. e. With E and D as centers, and with a radius more than half the length of DE, draw two arcs intersecting at point F. f. Join points A and F. The angle formed by FAB is 90°. i.e.

FAB = 90°. g. Now the point G will be the point of intersection of the ray AF and the first arc (from step b). With points G & D as centers, with any radius more than half the length of GD, draw two arcs such that they meet at point H. h. By joining point H and A, we get the ray AH which forms 75° with ray AB. Hence HAB = 75°

(ii) Given, to construct an angle of 105° from the initial point of a ray.

Steps of Construction:

a. Draw a ray AB of any length. b. Now as point A is the initial point as the centre, draw an arc any radius such that, the arc meets the ray AB at point C. c. With C as centre and with the same radius as before, draw another arc cutting the previous one at point D. d. Now with D as centre and with the same radius, draw an arc cutting the first arc (drawn in step ii) at point E. e. With E and D as centers, and with a radius more than half the length of DE, draw two arcs intersecting at point F. f. Join points A and F. The angle formed by FAB is 90°. i.e.

FAB = 90°. g. Now the point G will be the point of intersection of the ray AF and the first arc (from step b). With points G & E as centers, with any radius more than half the length of GE, draw two arcs such that they meet at point H. h. By joining point H and A, we get the ray AH which forms 105° with ray AB. Hence HAB = 105°

(iii) Given, to construct an angle of 135° from the initial point of a ray.

Steps of Construction:

a. Draw a ray AB of any length. b. Now as point A is the initial point as the centre, draw an arc any radius such that, the arc meets the ray AB at point C. c. With C as centre and with the same radius as before, draw another arc cutting the previous one at point D. d. Now with D as centre and with the same radius, draw an arc cutting the first arc (drawn in step ii) at point E. e. With E and D as centers, and with a radius more than half the length of DE, draw two arcs intersecting at point F. f. Join points A and F. The angle formed by FAB is 90°. i.e.

FAB = 90°. g. Now extend AB to the left till point X. With A as centre and with some convenient radius draw an arc which intersects ray AF at G and AX at H. h. With H and G as centers and with any radius more than half of the length of GH, draw two arcs intersecting each other at I. i. Join I and A. The angle formed by ray IA and AB is 135°. Hence IAB = 135°

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