Question

Construct an angle of 90 at the initial point of a given ray and justify the constriction

Answer 1

Answer:

Step I : Draw AB¯¯¯¯¯¯¯¯.

Step II : Taking O as centre and having a suitable radius, draw a semicircle, which cuts OA¯¯¯¯¯¯¯¯ at B.

Step III : Keeping the radius same, divide the semicircle into three equal parts such that BC˘=CD˘=DE˘ .

Step IV : Draw OC¯¯¯¯¯¯¯¯ and OD¯¯¯¯¯¯¯¯.

Step V : Draw OF¯¯¯¯¯¯¯¯, the bisector of ∠COD.

Step-by-step explanation:

Answer 2

JUSTIFICATION:-

$\large\tt\underline\red{STEP\:1}$

Join AD, CD, DE and AE

$\large\tt\underline\red{STEP\:2}$

By construction,AC=AD=CD

$\therefore$$\small\sf{∆DAC\:is\:equilateral\:∆}$

& $\large\sf{\angle{DAC}=60°}$

$\large\sf\green{AD=DE=AE=60°}$

$\therefore$$\small\sf{∆ADE\:is\:a\:equilateral\:∆}$

$\large\sf{and\:\angle{DAE}=60°}$

$\small\tt\underline\purple{AF\:is\:the\:angle:bisector\:of\:DAE}$

$\therefore$$\large\sf{DAF = \frac{1}{2} \times 60°}$

$\large\sf{DAF=30°}$

$\therefore$$\large\sf{\angle{DAC}+\angle{DAF}=60+30}$

$\longrightarrow$$\large\sf{90°}$