Question

construct an angle 90 degree at the initial point of a given ray and justify the construction ​

Answer 1

The steps of construction to follow:

Step 1: Draw a ray OP.

Then, take O as the centre and any radius draw an arc cutting OP at Q.

Step 2: Now, taking Q as the centre and with the same radius as before draw an arc cutting the previous arc at R. Repeat the process with R to cut the previous arc at S.

construction

Step 3: Take R and S as centre draw the arc of radius more than the half of RS and draw two arcs intersecting at A. Then, join OA.

Hence, poa =90°

Answer 2

I can't draw but I gave the step of construction

l hope it will help you.

Step 1: Draw a ray OP.

Then, take O as the centre and any radius draw an arc cutting OP at Q.

Step 2: Now, taking Q as the centre and with the same radius as before draw an arc cutting the previous arc at R. Repeat the process with R to cut the previous arc at S.

Step 3: Take R and S as centre draw the arc of radius more than the half of RS and draw two arcs intersecting at A. Then, join OA.

Hence, .

Justification:

We need to justify, 

So, join OR and OS and RQ. we obtain

By construction OQ = OS = QR.

So,  is an equilateral triangle. Similarly  is an equilateral triangle.

So, 

Now,  that means .

Then, join AS and AR:

Now, in triangles OSA and ORA:

  (common) 

  (Radii of same arcs)

  (radii of the same arcs)

So, 

Therefore, 

and