Q. 44.2( 169 Votes )

# Construct the following angles and verify by measuring them by a protractor:

(i) 75°

(ii) 105°

(iii) 135°

Answer :

(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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