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Question

# Draw an angle of 80∘ using a protractor and divide it into four equal parts, using ruler and compasses. Check your construction by measurement.

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Solution

## Steps of construction:Step I- With the help of protractor, draw an angle of 80∘. Name the rays OA and OB.Step II - Cut OA and OB at Q and P, taking O as the center and any convenient radius, with the help of the compass.Step III - With vertex P, by using compass take more than half of arc PQ and draw arc.Step IV - With vertex Q, by using compass with same length, cut the previous arc at R.Step V- With help of ruler, join the point O and R.∴ ∠AOR=∠ROBStep VI - Similarly, bisect the arcs QS and SP∴ ∠AOV=∠VOR and ∠ROU=∠UOBThus, ∠AOV, ∠VOR, ∠ROU and ∠UOB divide ∠BOA in four equal partsYou can verify this by using a protractor.∴ ∠AOV=∠VOR=∠ROU=∠UOB=20∘Hence, required construction is formed.

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