Question

construct the angle of the following measurements : (a) 30°​

Answer 1

Answer:

(i) We need to construct an angle of 60 degrees and then bisect it to get an angle measuring 30°.

Steps of Construction:

Construct the angles of the following measurements: (i) 30° (ii) 221/2° (iii) 15°

a) Draw a ray PQ.

b) To construct an angle of 60°, with P as a center and any radius, draw a wide arc to intersect PQ at R. With R as a center and same radius, draw an arc to intersect the initial arc at S. Then, ∠SPR = 60°

c)To bisect ∠SPR, with R and S as centers and radius greater than half of SR, draw two arcs to intersect at T. Join P and T

So, PT is the angle bisector. Hence, ∠TPR = 1/2 ∠SPR =30°

ii) We need to construct two adjacent angles of 60° and bisect the second one to get a 90° angle. This has to be bisected again to get a 45° angle. The 45° angle has to be further bisected to get

22

1

2

° angle.

22

1

2

° = 45°/2

45° = 90°/2 = (30° + 60°)/2

Answer 2

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➻ Refer to the attachment

✯ Steps to draw 30° are as follows :-

• Draw a ray OX.
• Cut an arc from O, cut another arc of same length as OA, which intersects at B.
• Cut two arcs from A and B which intersects at C.
• Join O - C.
• ∠COA is 30°