# Important Questions for Chapter 11 - Constructions

The CBSE Important Questions for Maths from grades 6th to 10th will help you in preparing for your exams, solving homework questions or learning concepts as well. These solutions are available for free. Download now!

**Important questions based on NCERT syllabus for Chapter 11 - Constructions:**

*Question 1*: Construct a 60∘ angle using a line segment of length of length 10 cm.

*Solution*:

Steps :

- Draw a line segment AB of length 10 cm.
- With A as centre draw an arc of any radius. Let this arc intersect AB at P.
- With the same radius as before draw an arc with P as centre. Let this arc cut the previously drawn arc at Q.
- Angle QAP is the required the 60∘ angle.
- QA makes angle of 60∘ with line segment AB whose length is 10 cm.

*Question 2*: Construct 75∘ and verify by measuring it by a protractor.

*Solution*:

Steps :

- Take the given ray PQ . Draw an arc of some radius taking point P as its centre, which intersects PQ at R.
- Taking R as centre and with the same radius as before , draw an arc intersecting the previously drawn arc at S.
- Taking S as centre and with the same radius as before, draw an arc intersecting the arc at T.
- Taking S and T as centre, draw an arc of same radius to intersect each other at U.
- Join PU. Let it intersect the arc at V. Taking S and V as centre, draw arcs with radius more than 12SV.
- Let those intersect each other at W. Join PW which is the required ray making 75∘ with given ray PQ.

The angle so formed can be measured with the help of a protractor. It comes to be 75∘

*Question 3*: Construct a triangle ABC in which BC is 3 cm, ∠ B is 60∘ and AC - AB = 1 cm.

*Solution*:

Steps :

- Draw a line segment BC = 3cm. Draw ray BX which makes an ∠60∘ with BC.
- Cut off line segment BD of length AC - AB = 1 cm on BX on the opposite side of BC. Join CD.
- Draw the perpendicular bisector of CD. Let the perpendicular bisector intersect ray BX at A.
- Triangle ABC is the required triangle.