# QUESTION VIDEO: USING ANGLE MEASURES TO FIND THE NUMBER OF PARTIAL TURNS IN A FULL TURN

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

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. 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.

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