Question

Construct an angle of 90° at the initial point of a given ray and justify the construction.

Please help please please. ​

Answer 1

Justification

Join OC and BC

Thus,

OB=BC=OC [Radius of equal arcs]

∴△OCB is an equilateral triangle

∴∠BOC=60 o

Join OD,OC and CD

Thus,

OD=OC=DC [Radius of equal arcs]

∴△DOC is an equilateral triangle

∴∠DOC=60 o

Join PD and PC

Now,

In △ODP and △OCP

OD=OC [Radius of same arcs]

DP=CP [Arc of same radii]

OP=OP [Common]

∴△ODP≅△OCP [SSS congruency]

∴∠DOP=∠COP [CPCT)

DOP=∠COP= 21

∠DOC

∠DOP=∠COP= 21×60=30 o

Now,

∠AOP=∠BOC+∠COP

∠AOP=60+30

∠AOP=90 o

Hence justified & construction in the above attachment ☑️

$MARK AS BRAINLIEST☑️$