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Mathematics

Using only ruler and compass, construct an angle of 90°. Then construct an angle of 45° by bisecting it.

Constructions

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Answer

Steps of construction :

  1. Draw a line l. Mark two points O and A on the line l.

  2. With O as centre and a convenient radius, draw an arc cutting OA at P.

  3. With P as centre and the same radius, cut the arc at Q. With Q as centre and the same radius, cut the arc again at R.

  4. With Q and R as centres and radius more than half of QR, draw two arcs intersecting at S. Join OS. Then ∠AOS = 90°.

  5. To get 45°, bisect ∠AOS : with P and the point M, as centres, draw two arcs intersecting at T. Join OT. Then ∠AOT = 45°.

Using only ruler and compass, construct an angle of 90°. Then construct an angle of 45° by bisecting it. Model Question Paper, ML Aggarwal Understanding Mathematics Solutions ICSE Class 6.

Hence, ∠AOS = 90° and on bisecting it, ∠AOT = 45° is constructed.

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