In geometry, learning how to construct a 75 degree angle with a compass is very useful in learning various concepts of geometry like Understanding how different angles combine and how to accurately create specific angles. It also helps in learning the fundamental geometric constructions, such as bisecting angles and constructing perpendicular lines.

Although 75° angle can be quickly drawn by using a protractor, this is an essential skill for students to accurately construct 75° angle with a compass and ruler.

What is a 75 degree angle?

A 75° angle, is an acute angle formed by the meeting of line segments. In other words a 75 degree angle is angle that measures 75 degree on the protractor which means the separation between the lines is 75 degree.

Materials Required

The materials required to construct a 75 degree angle are:

• Compass: The compass is an important instrument to use when making a 75-degree angle, as it will be used to measure and draw the arcs quite correctly.
• Ruler: A ruler will be used to take a proper reading and draw straight lines of an appropriate measure of length.
• Pencil: A sharp pencil is required to mark points, describe lines, and write comments on the paper.
• Clean Sheet of Paper: All the lines and markings are drawn on a plane and smooth surface also the angle will be drawn on the sheet of paper.

Step-by-step instructions to Construct a 75-degree angle using a compass :

Draw the Initial Line Segment: Use your ruler to draw a horizontal line segment. Let’s denote this segment as OA, where O is the starting point (origin) and A is the endpoint.

Step 1: Construct an Angle of 75 Degree using Compass

Construct a 60-degree Angle

• Place the compass pointer at point O (origin).

• Adjust the compass to a suitable radius and draw an arc that intersects OA. Let’s denote this intersection point as C.

Step 3: Construct an Angle of 75 Degree

• Without changing the compass radius, place the compass pointer at point C and draw another arc intersecting the first arc. Let’s denote this intersection point as D.

Step 3: Construct an Angle of 75 Degree

Draw a perpendicular passing from E and joining OA.

Step 4: Construct an Angle of 75 Degree

Construct a 75-degree Angle

• By intersecting 60 degree angle and 90 degree angle.

Step 5: Construct an Angle of 75 Degree

Draw the Angle

Use a ruler to draw a line from point O through point H. This line will form a 75-degree angle with OA.

Step 6: Construct an Angle of 75 Degree using Compass

Verify the Angle

Double-check using a protractor or geometric principles that the angle formed measures 75 degrees.

Important tips while Constructing 75 Degree Angle

Here are some important tips to ensure the construction of perfect 75 degree angle:

• Use a sharp pencil to draw the line with precision and care as dull pencils may result in fuzz or an unclear intersection.
• Use a proper ruler to measure the line well, and draw a straight line.

• While adjusting the width of the compass, make sure that it is more than half the length of AB.

• While drawing the arcs, the compass should be held tightly so it does not waver or slip so measurements are accurate also ensure that the width of the compass remains unchanged while drawing the arc.

• Link the points of intersection and draw a straight line with the use of a ruler through the points of intersection. Ensure that the line drawn is a bit longer than the point of intersection at both extremes so that it gives a clear, sharp, and perpendicular line.

Conclusion

This method to construct 75 degree angle using compass leverages geometric principles of angles and the compass to accurately construct a 75-degree angle using basic tools like a compass and ruler. Adjusting the compass carefully and ensuring accurate intersections are crucial for achieving the desired angle.

Construct an Angle of 75 Degree using Compass – FAQs

Why use a 60-degree angle to construct a 75-degree angle?

Using a 60-degree angle allows us to apply geometric principles effectively. By bisecting the 60-degree angle, we create a 30-degree angle. Adding 45 degrees to this gives us a total of 75 degrees, ensuring accuracy in angle construction.

How do you ensure precision when using a compass to draw arcs?

Precision with a compass is crucial. Ensure the compass radius remains consistent throughout each step. Double-check intersections where arcs meet to accurately pinpoint points like B and D. This ensures the final angle drawn is indeed 75 degrees.

Can this method be used to construct angles other than 75 degrees?

Yes, this method leverages geometric principles applicable to constructing various angles. By adjusting the initial 60-degree angle and subsequent steps, you can construct angles such as 15, 30, 45, 75 degrees, and beyond, depending on your needs and geometric understanding.