By using a ruler and compass, construct an angle of 135° and bisect it. Measure any one part by protractor and see how accurate you are.
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Question

By using a ruler and compass, construct an angle of 135° and bisect it. Measure any one part by protractor and see how accurate you are.

KnowledgeBoat · Accepted Answer

Steps: 1. Draw a straight line AOA'. 2. Construct a perpendicular OC to line AOA' at O. Then ∠AOC = 90°. 3. Bisect ∠A'OC by drawing two equal arcs from centre O, cutting line OA' at point D and OC at point E. Now, from points D and E draw two arcs of equal length intersecting each other at point B. Join OB and OB is the bisector of ∠A'OC. Then ∠COB = 45°. 4. Therefore, ∠AOB = ∠AOC + ∠COB = 90° + 45° = 135°. 5. Now bisect ∠AOB. With O as centre, draw two equal arcs that cut OA at point P and OB at point Q. 6. With P and Q as centres and equal radii , draw two arcs cutting each other at R. 7. Join OR and produce it to form ray OR. Then OR is the bisector of ∠AOB. On measuring one of the parts with a protractor, we find: ∠AOR = 67.5° (and ∠ROB = 67.5°). Hence, ray OR bisects ∠AOB into two equal parts of 67.5° each.

Mathematics

By using a ruler and compass, construct an angle of 135° and bisect it. Measure any one part by protractor and see how accurate you are.

Constructions

Related Questions

Draw ∠AOB = 76° with the help of a protractor. Bisect this angle by using a ruler and compass. Measure the two parts by your protractor and see how accurate you are.