Construct an angle of 67-5- by using the ruler and compasses-

Steps of Construction: 1. Draw a line TS. 2. Construct ∠ POS = 90°. 3. Draw OQ, bisector of ∠ POT. Thus, ∠ QOS = 135° is obtained. 4. Draw the bisector of ∠ QOS ...

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Byju's Answer

Standard IX

Mathematics

Construction of an Angle Bisector

Construct an ...

Question

Construct an angle of ${67.5}^{\circ}$ by using the ruler and compasses.

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Solution

Steps of Construction:
(i) Draw $∠ E O D = 90^{\circ}$
(ii) Now, bisect $∠ E O A = 120^{\circ}$ and $∠ B O A = 180^{\circ}$ to get $∠ G O A = 150^{\circ}$
(ii) Now bisect $∠ E O A = 120^{\circ}$ and $∠ G O A = 150^{\circ}$ to get $∠ F O A = 135^{\circ}$
(iii) Bisect $∠ F O A = 135^{\circ}$ to get $∠ C O A = {67.5}^{\circ}$

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Q. Which of the following angles can be constructed using ruler and compass only?
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Construct an angle of 67.5∘ by using the ruler and compasses.

Steps of Construction:(i) Draw ∠EOD=90∘ (ii) Now, bisect ∠EOA=120∘ and ∠BOA=180∘ to get ∠GOA=150∘(ii) Now bisect ∠EOA=120∘ and ∠GOA=150∘ to get ∠FOA=135∘(iii) Bisect ∠FOA=135∘ to get ∠COA=67.5∘

Construct an angle of ${67.5}^{\circ}$ by using the ruler and compasses.