Sum

Construct angle ABC = 45° in which BC = 5 cm and AB = 4.6 cm.

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#### Solution

**Steps of Construction :**

- Draw a line segment BC = 5 cm
- Taking B as centre, draw an arc of any suitable radius, which cuts BC at the point D.
- With D as the centre and the same radius, as taken in step 2, draw an arc which cuts the previous arc at point E.
- With E as the centre and the same radius, draw one more arc which cuts the first arc at point F.
- With E and F as centres and radii equal to more than half the distance between E at F, draw an arc which cut each other at point P.
- Join BP to meet EF at L and produce to point O. Then ∠OBC = 90°
- Draw BA, the bisector of angle OBC. [With D, L as centres and suitable radius draw two arc meeting each other at Q produced it to R]

=> ∠ABC = 45° [∴ BA is bisector of ∠OBC ∴ ∠ABC = = 45°] - From BR cut arc AB = 4.6 cm

Concept: Construction of an Angle

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