The DAV Class 6 Maths Book Solutions and **DAV Class 6 Maths Chapter 14 Worksheet 3 **Solutions of Constructions offer comprehensive answers to textbook questions.

## DAV Class 6 Maths Ch 14 WS 3 Solutions

Question 1.

Draw the following angles using ruler and compasses. Also label them:

(a) 60°

Answer:

Draw a ray AB.

Draw an arc with centre A and any suitable radius intersecting AB at D.

Taking D as centre and radius equal to the radius same as in step 2, draw an arc intersecting the first arc at E.

Join AE and produce to C. Then ∠CAB = 60°

(b) 120°

Answer:

Draw a ray AB.

Taking A as centre and with suitable radius, draw an arc intersecting AB at D.

Draw an arc with centre D and radius equal to first arc intersecting it at E.

Draw one more arc with centre E and the radius equal to first, intersects the previous arc at F. Join AF and produce to C.

Then ∠CAB = 120°.

(c) 90°

Answer:

Draw a ray AB.

Draw an arc with centre A and suitable radius + intersecting it at D.

Draw an arc with centre D and radius equal to first, intersecting the previous arc at E.

Draw another arc with centre E and radius equal to the previous arc intersecting it at F.

Taking E and F as centres and suitable radius, draw to circles intersecting each other at G.

Join AG and produce to C. Then ∠CAB = 90°.

(d) 45°

Answer:

Draw a ray AB.

Take A as centre and draw an arc cutting AB at P.

Taking P as centre, mark an arc at Q and then mark another arc at R taking Q as centre.

Draw two arcs taking R and Q as centres with the same radius which cut each other at S.

Join AS and produce to D such that ∠DAB = 90°. Draw AC as the bisector of ∠DAB.

Hence ∠CAB – 45°.

(e) 30°

Answer:

Draw a ray AB.

Taking A as centre draw an arc meeting AB at P. With the same radius taken in step 2 and with centre P, mark an arc Q.

Join AQ and produce to C such that ∠CAB = 60°. Draw AR as the bisector of ∠CAB.

Hence ∠CAR = 30°.

(f) 180°

Answer:

Draw a straight line AB.

Take any point 0 on AB.

Hence ∠AOB = 180°.

Question 2.

Construct an angle of 30° using compasses and ruler. Now construct an angle of measure 15° using compasses.

Answer:

Step 1: Draw a ray PQuestion

Step 2: Draw an arc with centre P and suitable radius intersecting it at A.

Step 3: Draw an arc with centre A and radius equal to first, intersecting the previous arc at B.

Step 4: With A and B as centres and suitable radius, draw two arcs intersecting at C.

Step 5: Join PC and produce to R such that ∠RPQ = 30°.

Step 6: Draw PS as the bisector of ∠RPQ with similar method.

Then ∠SPQ = 15°

Question 3.

Construct an angle of measure 22 \(\frac{1}{2}\)° using compasses and ruler

Answer:

Step 1: Draw a ray AB.

Step 2: Draw an arc with centre A and with suitable radius intersecting AB at P.

Step 3: Take P as centre and radius equal to the radius taken in step 2, draw an arc intersecting the first at Question

Step 4: Draw similar arc with centre Q and same radius to intersect the previous arc at R.

Step 5: With centres R and Q and suitable radius, draw two arcs intersecting each other at S.

Step 6: Join AS and produce to C such that ∠CAB = 90°.

Step 7: Draw AD as the bisector of ∠CAB such that ∠DAB = 45°.

Step 8: Draw AE as the bisector of ∠DAB such that ∠EAB Jo

Hence ∠EAB = 22\(\frac{1}{2}\)°