Draw an angle of 152° and divide it into four equal parts.

Question

KnowledgeBoat · Accepted Answer

Steps: 1. Draw a ray OA. 2. Place the centre of the protractor at O and the zero line along OA. Mark a point at 152°. 3. Remove the protractor and join O with the marked point and produce it to B. Then ∠AOB = 152°. 4. With O as centre and any (suitable) radius, draw an arc to meet ray OA at C and ray OB at D. 5. With C and D as centres, draw arcs of equal radius cutting each other at E. Join OE and produce it. Then OE bisects ∠AOB, so ∠AOE = ∠EOB = 76°. 6. Let OE meet the first arc at point F. 7. Now bisect ∠AOE: with C and F as centres, draw arcs of equal radius cutting each other at G. Join OG and produce it. 8. Similarly, bisect ∠EOB: with F and D as centres, draw arcs of equal radius cutting each other at H. Join OH and produce it. Then OG bisects ∠AOE and OH bisects ∠EOB. Therefore, ∠AOG = ∠GOE = ∠EOH = ∠HOB = 38°. and ∠AOE = ∠AOG + ∠GOE = 76 ∠EOB = ∠EOH + ∠HOB = 76 Hence, the angle of 152° is divided into four equal parts each of measure 38°.

Mathematics

Draw an angle of 152° and divide it into four equal parts.

Constructions

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