Question

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∠abc is shown. place the steps for constructing a copy of the angle in the correct order with the first step at the top and the last step at the bottom. place the compass on point b, set to any convenient width. draw an arc across both sides of the angle, creating the points j and k. without changing the compasss width, place the compasss point on p and draw a similar arc there, creating point m where the arc crosses pq. set the compass on k and adjust its width to point j. make a point p that will be the vertex of the new angle. from p, draw a ray pq. this will become one side of the new angle. without changing the compasss width, move the compass to m and draw an arc across the first one, creating point l where the two arcs cross. draw a ray from p through l and onwards a little further. the exact length is not important.

Explanation:

Step1: Create vertex and one side

Make a point \( P \) that will be the vertex of the new angle. From \( P \), draw a ray \( \overrightarrow{PQ} \). This will become one side of the new angle.

Step2: Draw arc on original angle

Place the compass on point \( B \), set to any convenient width. Draw an arc across both sides of the angle, creating the points \( J \) and \( K \).

Step3: Draw corresponding arc on new side

Without changing the compass's width, place the compass's point on \( P \) and draw a similar arc there, creating point \( M \) where the arc crosses \( \overrightarrow{PQ} \). Set the compass on \( K \) and adjust its width to point \( J \).

Step4: Complete the angle construction

Without changing the compass's width, move the compass to \( M \) and draw an arc across the first one, creating point \( L \) where the two arcs cross. Draw a ray \( \overrightarrow{PR} \) from \( P \) through \( L \) and onwards a little further. The exact length is not important.

Answer:

1. Make a point \( P \) that will be the vertex of the new angle. From \( P \), draw a ray \( \overrightarrow{PQ} \). This will become one side of the new angle.
2. Place the compass on point \( B \), set to any convenient width. Draw an arc across both sides of the angle, creating the points \( J \) and \( K \).
3. Without changing the compass's width, place the compass's point on \( P \) and draw a similar arc there, creating point \( M \) where the arc crosses \( \overrightarrow{PQ} \). Set the compass on \( K \) and adjust its width to point \( J \).
4. Without changing the compass's width, move the compass to \( M \) and draw an arc across the first one, creating point \( L \) where the two arcs cross. Draw a ray \( \overrightarrow{PR} \) from \( P \) through \( L \) and onwards a little further. The exact length is not important.