To construct a 90-degree angle (a right angle) using a compass and straightedge, you can follow these steps:-

  1. Draw a base line:- Start by drawing a straight line, which will be the base for your angle.
  2. Place the compass at one endpoint:- Place the compass point (the sharp end) on one endpoint of the base line.
  3. Adjust the compass width:- Open the compass to a width greater than half the length of the base line. This will ensure that the arc you draw will intersect the base line on both sides.
  4. Draw an arc:- With the compass set, draw an arc that intersects the base line.
  5. Place the compass at the other endpoint:- Move the compass point to the other endpoint of the base line.
  6. Draw another arc:- Without changing the compass width, draw another arc from the second endpoint. This arc should intersect the first arc you drew.
  7. Draw the angle bisector:- The intersection of the two arcs should form an angle bisector. Draw a straight line from the initial endpoint through the intersection point to the other side of the base line.
  8. Measure the angle:- The angle formed by the intersection of the base line and the bisector is a 90-degree angle, which is a right angle.

This construction utilizes the perpendicular bisector property to create a right angle. Make sure to use a ruler to draw straight lines and a compass to create accurate arcs.

Another way of Construction of 90⁰ Angle:-

Steps are -

Step.1) Draw any line l, and take a point O on it.

Step.2) With zero (0) as centre and suitable radius, draw an arc to cut the line l at the points A & B.


Step.3) With A & B as centres, draw two arcs of equal radius(> 1/2 AB) cutting each other at C.

Step.4) Join OC and produce it to form the ray OC, then -

                                            ∠BOC = 90⁰