We can use the angle bisector method to construct some other angles from existing angles.

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Examples:A 30° angle can be obtained by bisecting a 60° angle. A 15° angle can be obtained by bisecting a 30° angle. A 45° angle can be obtained by bisecting a 90° angle. A 22.5° angle can be obtained by bisecting a 45° angle.

How lớn construct a 45° angle by bisecting a 90° angle?

Example:The figure shows a point A on a straight line. Construct an angle of 45° at point A.


Solution:Construct a 90° angle, and then construct an angle bisector lớn obtain a 45° angle.

Step 1: Stretch your compasses until it is more then half the length ofAB. Put the sharp over at A và mark an arc above & another arc below line segment AB.


Step 2: Without changing the width of the compasses, put the sharp endat B và mark arcs above & below the line segment AB that will intersect with the arcs drawn in step 1.


Step 3: Join the two points where the arcs intersect with a straight line.This line is the perpendicular bisector of AB. P. Is the midpoint of AB.

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Step 4: Bisect the 90-degree angle to lớn forma 45-degree angle.


In summary the steps to construct a 45° angle are:

Construct perpendicular lines khổng lồ obtain a 90° angle.Bisect the 90° angle khổng lồ obtain a 45° angle.

How khổng lồ construct a 45-degree angle using compass và straightedge?Step 1: Construct perpendicular lines (90 degrees).

Step 2: Bisect that angle khổng lồ get a 45-degree angle.

How khổng lồ construct a 30-degree angle without using a protractor?This video shows two ways lớn construct a 30-degree angle.The first way starts by constructing part of an equilateral triangle, then bisecting the 60° angle.The second method starts by constructing a rhombus with 60° and 120° angles, then joining theopposite vertices khổng lồ leave the 30° angle.

How lớn construct a 75-degree angle with a compass?Step 1: Construct 60-degree angles by constructing an equilateral triangle.Step 2: Bisect a 60-degree angle to form a 30-degree angle.Step 3: Bisect the 30-degree angle to size a 15-degree angle.Step 4: Combine a 60-degree angle with a 15-degree angle to form a 75-degree angle.

Try the không tính tiền Mathway calculator and problem solver below khổng lồ practice various math topics. Try the given examples, or type in your own problem and kiểm tra your answer with the step-by-step explanations.


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