Constructing An Angle of 60 Degrees

In geometry, construction is the process of drawing a figure, shape, or many different types of angles. We draw such shapes using geometrical instruments like a compass, protractor, a ruler. While constructing angles we use a compass to draw arcs and a ruler to draw line segments and measure their lengths. We can draw an angle of 60 degrees using either of the two geometrical tools, a protractor or a compass. In this mini-lesson, we will learn how to construct an angle of 60 degrees using a protractor and a compass in detail.

Construction of angles with the help of a protractor is a very easy method. A protractor is a geometrical tool that can be used to measure as well as draw angles. Let us explore the steps which tell us about constructing an angle of 60-degrees with the help of a protractor.

Read the given steps and try it urself.

• Step 1: With the help of a ruler and pencil draw a line segment AB.
• Step 2: Now mark the center of the line segment as O.
• Step 3: Take a protractor and place the protractor at point O.
• Step 4: Now look for 60 degrees angle in the protractor (at the outer circle of the protractor), mark a dot, and name it C.
• Step 5: Now join the points O and C.
• Step 6: After joining the lines we will have ∠AOC = 60°.

Observe the given image of constructing an angle of 60 degrees using a protractor.

Note- 60 degrees angle is an acute angle, i.e., less than 90 degrees.

Construction of angles with the help of a compass is slightly difficult as compared to construction with the help of a protractor. A compass is a geometrical tool used to draw arcs and circles. Let us explore the steps which tell us about constructing an angle of 60-degrees with the help of a compass.

Suppose that you have a line L and some point A on L just like shown in the figure.

Now let us try to you construct a ray (or line) through A which is inclined at 60° to L.

• Step 1: Taking A as a center, place the needle of a compass on A and draw an arc of any radius length that intersects L at B as shown in the figure below.

• Step 2: Now, taking B as center and AB as radius, draw another arc that intersects the first arc at C:

• Step 3: Draw a ray (or line) through A and C. This will be inclined at 60° to L:

Here, AB = AC, since these are radii of the same circular arc. Also, BC = BA, since these too are radii of the same (second) circular arc. Thus, AB = BC = AC. This means that triangle ABC is equilateral, and so, angle BAC = 60°.
Note that by bisecting an angle of 60°, we can construct an angle of 30°, and further by bisecting an angle of 30° we can construct an angle of 15°.

Related Articles on Constructing An Angle of 60 Degrees

Check out the interesting articles linked below to learn more about terminologies related to constructing an angle of 60 degrees.

• Essence of Geometrical Constructions
• Constructing Angle Bisectors
• Constructing Perpendicular Bisectors
• Constructing An Angle of 90 Degrees
• Constructing Perpendicular From Point to Line
• Protractor
• Acute Angles

How do you Construct a 60 Degree Angle?

We can construct a 60-degree angle using two geometrical instruments a protractor and a compass. Let us first look at the procedure we need to follow while constructing a 60-degree angle using a protractor. With the help of a ruler and pencil draw a line segment. Now mark the center on the line segment. Take a protractor and place the protractor at the center point. Now look for 60 degrees angle in the protractor, mark a dot, and name it. Now join the marked point and center point with a straight line. After joining the line we will have angle = 60°.

How Do you Construct An Angle of 60 Degrees Without a Protractor?

With the help of a compass, we can draw a 60-degree angle without a protractor. Let us explore the procedure of constructing an angle of 60-degrees with the help of a compass. Draw any line A and mark some point O on the line. Taking O as a center, place the compass needle at point O and draw a complete semi arc of any radius length that intersects line A at some point. Name the point B. Now, taking B as center and OB as radius, draw another arc that intersects the first arc. Give a name to the point which is the intersection point of the two arcs. Let say C. Draw a ray (or line) through O and C. This will be inclined at 60° to Line A.

How Do you Construct an Angle of 60 Degree at the Initial Point of a Given Ray?

We can construct an angle of 60 degrees at the initial point of a given ray with the help of a protractor. Look for 60 degrees angle in the outer circle (if the line segment is pointing towards the left-hand side) or inner circle (if the line segment is pointing towards the right-hand side) of the protractor by placing the protractor at a given point. Mark a dot and label it. Now join the points. After joining the lines we will have an angle measure as 60°. Please note that a 60 degrees angle is always an acute angle.

How do you Bisect a 60 Degree Angle?

By constructing half of the 60-degree angle i.e. by constructing a 30-degrees angle we can bisect a 60-degree angle. This is possible by using a compass. Look at the steps given below to bisect a 60-degree angle with the help of a compass:

• Step 1: Draw a line segment of any measurement and name it. Let's say MN
• Step 2: With the help of a compass construct an angle = 60°.
• Step 3: From point M draw an arc on MN. Name it Q. Now, taking Q as center and MQ as radius, draw another arc that intersects the first arc at F. Draw a ray (or line) through M and join MF which is inclined at 60°. Extend the line till some point and name it G.
• Step 4: Bisect ∠GMN with the help of the compass, take any radius which meets line MN and MG at points Q and F.
• Step 5: Now, with the compass take a radius more than QF and draw one arc each from point Q and F respectively. 
• Step 6: Now we have the intersection of both arcs at point new point. Name it O.
• Step 7: Proceed MO and extend it till some point and name it Z
• Step 8: The obtained angle ∠ZMN is the bisector of ∠GMN.
• Step 9: ∠ZMN = 30° and ∠GMN = 60°.

How Many Arcs are Required to be Drawn to Construct an Angle of 60?

While constructing an angle of 60 degrees, we can see that a total of two arcs are required to be drawn to construct an angle of 60 degrees at one point. 

Is it Possible to Construct a Triangle Whose Angles are 60º, 70º, and 60º?

According to the angle sum property which says all the angles of triangles sum up to 180 degrees, it is NOT possible to construct a triangle whose angles are 60 degrees, 70 degrees, and 60 degrees as the sum of all the three angles is not equal to 180 degrees.