Draw And Measure Angles Using Protractor
In this section you are going to learn how to draw and measure angles using a protractor which is very important for us to know to have a complete understanding of protractor. Let us see how to draw an angle of 30º using a protractor.
- Draw a baseline AB.
- Align the baseline of the protractor with the line OB.
- In the inner readings, look for 30º and mark it as point C.
- Now using a scale, join O and C.
COB = 30°
To measure 220º, a reflex angle, we can write it as 180° + 40°. We can just flip the protractor along the baseline and then mark 40°.
180° + 40° = 220°
- We can also use a 360° protractor to draw this angle. The angle protractor tool and 360° protractor give more precise measurements.
- The symbol for the degree is . Always use it while writing the angles. Example
- If the angle to be measured is in the left side, use the outer readings of the protractor and if the angle to be measured is in the right side, use the inner readings.
- To reduce errors, align the baseline and vertex properly.
Constructing Angles With Compass And Ruler
Let us learn how to construct an angle with a compass and a ruler. In the steps shown below we will be constructing an angle of 90° and then construct an angle bisector to bisect the 90° such that we will get an angle of 45°.
- Step 1: Draw a ray AB.
- Step 2: With A as the center and any width as radius draw a semicircular arc that touches the line segment AB and mark it as Q.
- Step 3: Without any change in radius, draw another arc with Q as the center and label this point as D.
- Step 4: Repeat the same process with D as the center and label the arc drawn as E.
- Step 5: Now, with the same radius and with E and D as centers draw arcs that intersect each other at a point and label it as F.
- Step 6: Now join the points A and F. This line is called the perpendicular line and it makes 90 degrees with the line segment AB.
- Step 7: Label the point of intersection of the semicircular arc with the line AF as P.
- Step 8 – Now with the same radius taken to draw an arc in step 2, draw two arcs with P and Q as centers. Mark the point of intersection of these arcs as R. Now join the points A and R. Now RAB and FAR are equal to 45° each.
Measuring Angles With A Protractor
This 4th grade geometry lesson explains angle measure, how to measure angles with a protractor, and has varied exercises for the students.
The video below explains what an angle measure is, how to measure angles with a protractor, and how to draw angles with a protractor.
Remember how one side of the angle traces out a circular arc? We use that circle to measure how big the angle is. We look at how much the angle has opened as compared to the full circle.
Angles are measured in degrees. The symbol for degrees is a little circle °.
- The FULL CIRCLE is 360° .
- A half circle or a straight angle is 180°.
- A quarter circle or a right angle is 90°.
Show the angles below using two pencils. Try to see the circle that is traced out in the air.
This is a 1-degree angle!
an obtuse angle 127°
How to measure an angle with a protractor:
Take care to read from the right set of numbers. A protractor has two sets of numbers: one set goes from 0 to 180, the other set from 180 to 0. Which one you read depends on how you place the protractor: place it so that one side of the angle lines up with one of the zeros, and read that set of numbers.
In the examples above we lined up the one side of the angle with the zero of the lower set of numbers, so we need to read the lower set of numbers.
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How To Use A Protractor
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A protractor is a handy tool used to measure and draw angles. Generally, semi-circular in shape, protractors are also available in full-circle, 360-degree versions. If one look at the object has you completely confused, never fear learning to use the tool is simple. By understanding how the parts of a protractor are used together and following a few easy steps, you will be an angle expert in no time.
What Is A Protractor
The size of an angle is measured using a protractor. The shape of a protractor is a semicircle. The semicircle is divided into two parts. The protractor has two sets of measurements. The first set is from 0° to 180° and the other set is from 180° to 0°. The marking on the inner circle is 0 degrees to 180 degrees in the opposite direction to the markings on the outer circle.
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Construction Of 30 Degrees Using Compass
An angle of 30 degrees can also be constructed using a compass. Now let us see how to construct a 30-degree angle using a compass, ruler, and a pencil. Follow the steps given below:
- Draw a ray AB. With A as the center and a suitable radius on the compass draw a semicircular arc such that it touches the line segment AB at a point C.
- With C as the center and without any change in the radius, draw an arc that cuts the semicircular arc at point D.
- With C and D as the center, draw two arcs that intersect each other and label it as E.
- Join the points A and E. Here, EAB = 30°.
The construction of the angle of 30° using a compass is shown below.
How Do You Draw A 30
To draw a 30-degree angle using the protractor, follow these steps:
- Step 1: Draw a line segment OA.
- Step 2: Place the center tip of the protractor at point A such that the protractor perfectly aligns with line AO.
- Step 3: Start from 0 on the protractor in the clockwise direction and stop at 30. Mark the point D.
- Step 4: Join point D with A. DAO=30° is the required angle.
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Angle Activity With Online Protractor
This activity allows manipulation and investigation of varioustypes of angles. The online protractor tool can be used to practice measuring angles.It can be used at a variety of different gradelevels. At its most basic for teaching about types of angles, acute,obtuse or reflex. For more advanced use to create angle problems inwhich the missing letter angle values have to be found. You can click and drag thehandles to change the angles and the values will updated.
Constructing Angles Using A Protractor
An angle can be constructed either by using a protractor and a ruler or a compass and a ruler. Let us now look at the steps of constructing a 50° angle using a protractor.
- Step 1 – Draw a line segment OA.
- Step 2 – Place the center of the protractor at point O.
- Step 3 – Starting from point A in the clockwise direction and mark a point at 50 degrees by looking at the outer circle of the protractor. Label this point as B.
The BOA is the required 50° angle.
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How To Measure Angles Using Protractor
A protractor is a semi-circular tool used to draw and measure angles. It is marked with degrees from 0 to 180 degrees. It can be directly used to measure any angle from 0 to 360 degrees. The markings are made in two ways, 0 to 180 degrees from right to left and vice versa.
Suppose we have an angle to measure say, ABC. Follow the steps given below to measure the angle.
Step 1. Put the protractor above the line BC such that the midpoint of protractor is at point B.
Step 2. Adjust the protractor in such a way that BC is parallel to the straight-edge of the protractor.
Step 3. The protractor has two scales marked from 0 to 180 degrees on both the ends. Take the reading where BC coincides with the 0 degree.
Step 4. Now from 0 degrees, check the ray BA coincides with the curved edges of the protractor. This reading gives us the measure of angle ABC.
How To Draw Angles Exceeding 180 Using A Semicircular Protractor
Although drawing angles more than 180° using a regular semicircular protractor may seem like a tough job, it isnt so. You can learn this in four simple steps. Here they are.
STEP 1Begin by drawing a line such that you leave ample space at the top and bottom of the line. Then, mark a vertex, and measure 180° using your protractor.
STEP 2Once measured, draw a dotted line from the vertex to the marked point.
STEP 3Now flip the paper, and hold the protractor once again on the marked vertex. Considering the dotted line as your base line, and 0° as 180°, mark the desired angle. For instance, if you wish to draw an angle measuring 260°, begin counting from 180 to 260. So, 260° will be an additional 80° from 0.
STEP 4After youve marked the said angle, draw a line connecting the vertex and the marked point. Then, flip the paper, and you have your desired angle exceeding 180° without using a circular protractor.
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How To Draw Angles With A Protractor
Protractors can also be used to draw an angle having a specific measure. For example, to draw OMP having a measure of 30°:
- First, draw a line segment OM and put the protractor on the line such that vertex M lies on the midpoint of the protractor and OM lines up with the 0 line on the left side of the protractor.
- Then find 30 on the outside set of degree measures and mark it with point P.
- Lastly, draw segment MP with a straight edge. It’s ok to extend the segment beyond P.
We could also construct OMP by placing OM on the 0 degree line on the right side of the protractor as long as vertex M is centered at the midpoint of the protractor. Similarly, we could have constructed OM on the 0-degree line first then placed point O on the 30 degree measure to draw OM.
How Do You Measure And Construct Angles
An angle can be measured using a protractor which is a semi-circular disc used to draw and measure angles. Most protractors measure angles in degrees and are divided into 180 equal parts. They can be directly used to measure any angle within the range of 0° to 180° using the markings. We can use either protractor or a compass to construct angles of a specific measurement.
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Constructing Angles Using Protractor
Example 1 :
Construct an acute angle of 60°.
Step 1 :
Draw a line segment PA.
Step 2 :
Place the protractor on the line segment PA
Place the mid point of the protractor at point P as shown in the figure.
Step 3 :
On PA from the right start counting from 0° in the ascending order (counter clock wise direction and finally mark a point Q using a sharp pencil at the point showing 60° on the semi-circular edge of the protractor.
Remove the protractor and join PQ.
We get the required angle APQ = 60°.
Example 2 :
Construct an acute angle of 125°.
Step 1 :
Draw a line segment PA.
Step 2 :
Place the protractor on the line segment PA.
Place the mid point of the protractor at point P as shown in the figure.
Step 3 :
On PA from the right start counting from 0° in the ascending order and finally mark a point Q using a sharp pencil at the point between 120° and 130° showing 125° on the semicircular edge of the protractor.
Remove the protractor and join PQ.
We get the required angle APQ = 125°.
Apart from using protractor, we can construct angles using ruler and compass also.
To know how to construct angles using ruler and compass,
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Rules for Operations on Inequalities
How To Use A Protractor To Draw Angles
A protractor is a semi-circular tool used to draw and measure angles, from 0° to 180° in clockwise and anti-clockwise. If kids are familiar with drawing an angle with a protractor then they can easily draw an angle between 0° to 180°. Drawing Angles using a Protractor can be easy if you follow the below steps.
To construct an angle of any given measure, children can follow these simple steps.
Step 1: Draw a line segment of any length, and name both ends.
Step 2: Place the protractor at the start point of a line segment drawn.
Step 3: The protractor has two sets of markings. We examine the scale which has 0° near the endpoint of a line segment. Mark, another point next to the degrees given to measure or draw an angle and label the point.
Step 4: Finally, join both the points, i.e., the starting point of the line segment and the point marked using a protractor by a line. By joining three points we get a required angle.
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What Is An Angle
An angle is a shape in geometry that is formed when two rays are joined together at a single point. The point where two rays meet is called the vertex of the angle and two rays are called the arms of the angle.
There are different types of angles based on their measures, such as:
- Acute Angle: Formed between 0° to 90.
- Obtuse Angle: Formed between 90° to 180°
- Right Angle: The angle which is exactly equal to 90°
- Straight Angle: The angle which is exactly equal to 180°
- Reflex Angle: The angle which is greater than 180 degrees and less than 360 degrees
- Full Rotation: The complete rotation of angle equal to 360 degrees
Mode ‘one’ Identifying Angle Types
The initial mode is unique in that there is only one angle. This modeis great for identifying various types of angles. Click the angle type ctrl to either show or hide thetype. So now you can change the angle by dragging a handle or clickingdice for a random value. The angletypes definitions are listed in the glossary below.
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How To Construct An Angle Bisector
- Draw a given angle using a protractor . Let us name the vertices of the angle as A, B, and C such that angle ABC = 60 degrees.
- With B as the center and with more than half of BC as radius draw an arc on both the arms, which is AB and BC, and mark these points where the arc touches the line segments as D and E respectively.
- Now with D and E as the centers draw two arcs such that they intersect at a point. Label this point as F.
- Join F and B. FB is the angle bisector and now, ABF and FBC will measure 30 degrees each.
Construction Of Angles Using A Protractor Examples
Example 1.How to Construct 90 degrees using a protractor.Solution:Draw a line segment BC, which is one of the arms of the angle that is to be constructed.Place the protractor with its point O on the point B of the line segment BC.Align OQ along the edge BC.The protractor has two-way markings. We consider the scale which has 0 degrees near point C for construction. Mark point A next to the 90 degrees mark on the scale.Join points A and B. ABC = 90 degrees is the required angle.
Example 2.How to Construct 75 degrees using a protractor.Solution:Draw a line segment BC, which is one of the arms of the angle that is to be constructed.Place the protractor with its point O on the point B of the line segment BC.Align OQ along the edge BC.The protractor has two-way markings. We consider the scale which has 0 degrees near point C for construction. Mark point A next to the 75 degrees mark on the scale.Join points A and B. ABC = 75 degrees is the required angle.
Example 3.How to Construct 110 degrees using a protractor.Solution:Draw a line segment BC, which is one of the arms of the angle that is to be constructed.Place the protractor with its point O on the point B of the line segment BC.Align OQ along the edge BC.The protractor has two-way markings. We consider the scale which has 0 degrees near point C for construction. Mark point A next to the 110 degrees mark on the scale.Join points A and B. ABC = 110 degrees is the required angle.
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