# 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°

**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.