Selina solutions

Grade 7

# Question 1

Q1) Using ruler and compasses, construct the following angles :

(i)30°

(ii)15°

(iii) 75°

(iv) 180°

(v) 165°

(vi) 22.5°

(vii) 37.5°

(viii) 67.5°

Solution:

(i) 30°

Steps of Construction :

Draw a line segment BC.

With centre B and a suitable radius draw an arc meeting BC at P.

With centre P and with same radius cut off the arc at Q.

Now with centre P and Q draw two arcs intersecting each other at R

Join BR and produce it to A, forming ZABC

= 30°

(ii) (15°)

Steps of Construction:

Draw a line segment BC.

With centre B and a suitable radius draw an arc meeting BC at P.

With centre P and with same radius cut off the arc at Q.

Taking P and Q as curves, draw two arcs intersecting each other at D and join BD.

With centre P and R, draw two more arcs intersecting each other at S.

Join BS and produce it to A.

Then ∠ABC = 15°.

(iii) 75°

Steps of Construction :

Draw a line segment BC.

With centre B and a suitable radius draw an arc and cut off PQ, then QR of the same radius.

With centre Q and R, draw two arcs intersecting each other at S.

Join SB.

With centre Q and D draw two arcs intersecting each other at T.

Join BT and produce it to A.

Then ∠ABC = 75°.

(iv) 180°

Steps of Construction :

Draw a line segment BC.

With centre B and some suitable radius draw arc meeting BC at P.

With centre P and with same radius cut of arcs PQ, QR and then RS.

Join BS and produce it to A.

Then ∠ABC = 180°.

(v) 165°

Steps of Construction :

Draw a line segment BC.

With centre B and some suitable radius draw an arc meeting BC at P.

With centre P and same radius cut off arcs PQ, QR and then RS.

Join SB

With centres R and S, draw two arcs intersecting each other at M.

With centre T and S draw two arcs intersecting each other at L.

Join BL and produce it to A. Then ∠ABC = 165°

(vi) 22.5°

Steps of Construction :

Draw a line segment BC.

With centre B and some suitable radius, draw an arc meeting BC at P.

With centre P and some radius, cut off arcs PQ.

Bisect arc PQ at R and join BR.

Bisect arc QR at S and join BS.

Now bisect arc PR at T.

Join BT and produce it to A.

(vii) 37.5°

Steps of Construction :

Draw a line segment BC.

With centre B and some suitable radius, draw an arc meeting BC at P.

With centre P and same radius cut off arcs PQ and QR.

Now bisect arc QR at S and again bisect arc QS at T.

Bisect arc PT at K.

Join BK and produce it to A.

(viii) 67.5°

Steps of Construction :

Draw a line segment BC.

With centre B and some suitable radius, draw an arc meeting BC at P.

With centre P and with same radius, cut arcs PQ and then QR.

Bisect arc QR at K and again bisect arc QK at S.

Bisect again arc SQ at T.

Join BT and produce it to A.

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