Question

Construct the angles of the following measurements:

(i) 30° (ii) 15°​

Answer 1

Answer:

)

1. Draw a ray OX.

2. Cut an arc from O, cut another arc of same length as OA, which intersects at B.

3. Cut two arcs from A and B which intersects at C.

4. Join O−C. ∠COA is 30

∘

.

2)

1. Draw a ray OX.

2. Cut an arc from O, cut 2 another arcs of same length as OA, which intersects as B and F.

3. Cut two arcs from B and F which intersects at C. (∠COX=90 deg)

4. In the similar way, bisect ∠COX to get DOX which is 45 deg angle and then again bisect ∠DOX to get to get EOX .

6. Join O−E. ∠EOA is 22.5

∘

.

3)

1. Draw a ray OX.

2. Cut an arc from O, cut another arc of same length as OA, which intersects at B.

3. Cut two arcs from B and A which intersects at C. (∠COX=30 deg)

4. In the similar way, bisect ∠COX to get DOX.

6. Join O−D. ∠DOA is 15

∘

.

solution

Answer 2

(i)We construct angle of 30° , As :-

Step 1 ) Draw a line AB .

Step 2 ) Take any radius and center " A " draw an arc that intersect our line AB at " C " .

Step 3 ) Now with same radius and center is C , we draw another arc that meet our first arc at " D ". Join AD

Step 4 ) Now we draw two arc with same radius by taking center C and D , both arc intersect at " E "

Step 5 ) We join line AE ( AE is angle bisector of ∠ BAD ) , So we get ∠ BAE = 30° .

We can verification :-

We know : ∠ BAD = 60°

And

line AE is angle bisector of ∠ BAD .

So,

∠ BAE = ∠ EAD = 30°

Here are the steps to construct an angle of measure 15°:-

Step 1 : Draw a ray OA. Now taking O as centre and convenient radius draw an arc intersecting OA at B.

Step 2: Taking B as centre and with the same radius before draw an arc intersecting the previously drawn arc at C.

Step 3 : Taking B and C as centre, draw arcs of same radius to intersect each other at D.

Now ∠AOD = 30°. Let BC intersect OD at E.

Step 4: Taking E and B as centre, draw arcs of same radius to intersect each other at F. Join OF.

Thus ∠AOF = 15°.