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Constructing a Copy of an Angle of Unknown Measure

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Constructing a copy of an angle of unknown measure:

Suppose an angle (whose measure we do not know) is given and we want to make a copy of this angle. As usual, we will have to use only a straight edge and the compasses.

Given ∠A, whose measure is not known.

Step 1: Draw a line l and choose a point P on it.

Step 2: Place the compasses at A and draw an arc to cut the rays of ∠A at B and C.

Step 3: Use the same compasses setting to draw an arc with P as the centre, cutting l in Q.

Step 4: Set your compasses to the length BC with the same radius.

Step 5: Place the compasses pointer at Q and draw the arc to cut the arc drawn earlier in R.

Step 6: Join PR. This gives us ∠ P. It has the same measure as ∠ A.

This means ∠ QPR has the same measure as ∠BAC.

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