LEARN MATH STEP BY STEP THROUGH VERY EASY PROCESS

CONSTRUCTION OF COPY OF AN ANGLE

__CONSTRUCTION OF COPY OF AN ANGLE -__

**Constructing a copy of an angle involves creating an angle with the same measure as a given angle. Here's a step-by-step guide to constructing a copy of an angle using a compass and a straightedge:**

**Let's say you have angle ABC, and you want to construct an angle with the same measure.**

__Construction Steps:-__

__Draw the Given Angle:-__Use a ruler to draw the given angle, in this case, angle ABC.__Place the Compass on Vertex A:-__Open the compass wider than the width of the angle. Place the compass on the vertex A of the given angle.__Draw an Arc:-__Without changing the compass width, draw an arc that intersects both sides of the angle (AB and AC).__Label the Intersection Points:-__Label the intersection points of the arc with the sides of the angle as D and E.__Place the Compass on Point D:-__Without changing the compass width, place the compass on point D (the intersection point on one side of the angle).__Draw Another Arc:-__Draw an arc that intersects the first arc. Label the point of intersection as F.__Draw a Line Through Points A and F:-__Use a straightedge to draw a line through points A and F.__Angle Copy:-__The angle between AF and AD is a copy of the given angle ABC.

__Note:-__ This construction works because the intercepted arcs AD and DE are congruent, and thus the angles at the center of the arcs (angles BAD and BAE) are congruent. As a result, the angle formed by lines AF and AD is a copy of angle ABC.

**Always ensure that your constructions are precise, and use a sharp pencil and a good quality compass for accurate results.**

__Understanding by another way -__

**Let ∠AOB be angle whose measure is known and we want to make a copy of this angle. We want to construct an angle whose measure is equal to the measure of ∠AOB.**

__Steps Of Construction -__

__Step.1__) Take any point 'P' and through 'P', draw ray PQ.

__Step.2__) With 'O' as centre and any (suitable) radius, draw an arc to meet ray OA at C and ray OB at D.

__Step.3__) Taking P as centre and same radius (as in step.2), draw an arc to meet PQ at R.

__Step.4__) Measure the segment CD with compass.

__Step.5__) With R as centre and radius equal to CD, draw an arc to meet the previous arc at S.

__Step.6__) Join PS and produce it to form a ray OT, then ∠QPT = ∠AOB.