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

**Solution:**

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°

= 90°

**☛ Check: **NCERT Solutions for Class 9 Maths Chapter 11

**Video Solution:**

## 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

**Summary:**

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.

**☛ Related Questions:**

- Construct an angle of 45° at the initial point of a given ray and justify the construction.
- Construct the angles of the following measurements:(i) 30°(ii) 22(1/2)°(iii) 15°
- Construct the following angles and verify by measuring them by a protractor:(i) 75°(ii) 105°(iii) 135°
- Construct an equilateral triangle, given its side and justify the construction.

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