Construct an angle of 90° at the initial point of a given ray and justify the construction.
We need to construct two adjacent angles each of 60 degrees and bisect the second one to construct 90 degrees.
Steps of Construction:
(i) Draw a ray PQ.
(ii) To construct 60° angle, draw an arc of any radius with P as center intersecting PQ at R. With R as center and same radius, draw an arc intersecting the previous arc at S. ∠SPQ = 60°
(iii) To construct adjacent 60°, with S as the center and same radius, draw an arc as before intersecting the initial arc at T. ∠TPS will be 60°
(iv) To bisect ∠TPS, with T and S as centers and radius more than half of TS, draw two arcs to intersect each other at U. Join P and U.
∠UPS = 1/2 ∠TPS = 30°
(v) Now we get ∠UPQ of 90° at the initial point P.
∠UPQ = ∠UPS + ∠SPR
= 30° + 60°
Construct an angle of 90° at the initial point of a given ray and justify the construction
Maths NCERT Solutions Class 9 Chapter 11 Exercise 11.1 Question 1
It is given that we have to construct an angle of 90° at the initial point of a given ray. We have drawn the angle using a compass and ruler and justified the construction.
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