Question

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

Answer 1

Steps of Construction:-

1. Draw AB straight line.

2. Taking A as centre and any radius draw an arc and intersect AB at C.

3. Taking C as centre with same radius draw an arc which intersect at D.

4. With same radius taking D as centre, it intersects at E.

5. With centres E and D with same radius draw two arcs which meet both at F.

6. If AF is joined, AB straight line is the line in the point A with 90°,

i.e., AF.

In the above construction ∠DAB = 60° and ∠DAE = 60°.

Angular bisector of ∠DAE is AF.

∴ ∠DAF = ∠EAF = 30°

∴∠BAF = ∠DAB + ∠DAE = 60°+ 30°

∴∠BAF = 90°.