Construct an angle of 45° at the initial point of a given ray and justify the construction
Solution:
We need to construct two adjacent angles each of 60° and bisect the second one to construct 90°. Then, bisect the 90° angle to get 45°.
[60° + (60°/2)] / 2 = 45°
Steps of Construction:
(i) Draw ray PQ.
(ii) To construct an angle of 60°, with P as center draw a wide arc of any radius to intersect the ray at R. With R as a center and same radius draw an arc to intersect the initial one at S. Then ∠SPR = 60°.
(iii) To construct an adjacent angle of 60°, with S as the center and same radius draw an arc to intersect the previous arc at T. Then, ∠TPS = 60°
(iv) To bisect ∠TPS, with T and S as a center and radius more than half of ST, draw arcs to intersect each other at U.
(v) Join P and U. Then, ∠UPS = 1/2 ∠TPS = 30°
∠UPQ = ∠UPS + ∠SPR
= 30° + 60°
= 90°
(vi) To bisect ∠UPQ, with R and V as centers and radius greater than half of RV, draw arc to intersect each other at W. Join PW. PW is the angle bisector of ∠UPQ.
Then, ∠WPQ = 1/2 ∠UPQ = 1/2 × 90° = 45°
So, ray PW forms an angle of 45°with ray PQ at the initial point.
☛ Check: NCERT Solutions for Class 9 Maths Chapter 11
Video Solution:
Construct an angle of 45° at the initial point of a given ray and justify the construction
Maths NCERT Solutions Class 9 Chapter 11 Exercise 11.1 Question 2
Summary:
It is given that we have to construct an angle of 45° 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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