Constructing a Copy Of An Angle of Unknown Measure

Sometimes, we need to replicate an angle without knowing its exact measure. Follow these steps to construct a copy of a given angle.

Steps of Construction:

1. Draw a Reference Line:

• Draw a straight line and mark a point P on it. This will be the vertex of the new angle.

2. Draw an Arc on the Given Angle:

• Place the compass pointer at A (the vertex of the given angle ∠BAC).

• Draw an arc that intersects both rays (AC and AB) at points B and C.

3. Replicate the Arc on the New Angle:

• Without changing the compass width, place the compass pointer at P.

• Draw a similar arc intersecting the reference line at Q.

4. Measure the Distance Between the Intersections (BC):

• Set the compass width to the distance BC (the segment between the two intersection points on the given angle).

5. Transfer the Measurement to the New Angle:

• Place the compass pointer at Q and draw an arc that intersects the previous arc at R.

6. Complete the Angle:

• Join P to R with a straight line.

• ∠RPQ is the required angle, which is an exact copy of ∠BAC.

Thus, ∠QPR ≅ ∠BAC, meaning both angles have the same measure.