Mathematics
Construct ∠ABC = 75° using a protractor. Bisect this angle using a compass and ruler. Measure the two angles formed and verify.
Constructions
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Answer
Steps of construction:
(i) Draw a ray BC. With the help of a protractor, place its centre at B and mark a point at 75°. Join B to this point to obtain ray BA, so that ∠ABC = 75°.
(ii) With B as centre and a convenient radius, draw an arc cutting BA at P and BC at Q.
(iii) With P and Q as centres and a radius more than half of PQ, draw two arcs meeting at R.
(iv) Join BR. Then BR bisects ∠ABC.
Each of the two angles formed = = 37.5°.
On measuring with the protractor, ∠ABR = ∠RBC = 37.5°, and 37.5° + 37.5° = 75° = ∠ABC, which verifies the bisection.
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