Question

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

Answer 1

• Let AB be the given ray. 
• Produce BA to D. 
• Taking A as centre draw a semi circle with some radius. 
• With X and Y as Center draw two intersecting arcs of same radius.

Or

• Let \(\overrightarrow {AB}\)  be the given ray. 
• With A as centre draw an arc of any radius.
• Mark off two equal arcs from X as shown in the figure with the same radius taken as before. 
• Bisect the second segment. 
• Join the point of intersection of above arcs, with A. 
• ∠BAC is the required right angle. 
• Join the point of intersection ‘C’ and ‘A’. 
• ∠BAC = 90°

In ΔAXY; ∠YAX = 60° and 

in ΔAYC ∠YAC = 30° ∠BAC = 90°