Constructing Angles | How to Construct Angle with Protractor and Compass

Constructing Angles with a Protractor

Constructing angles is an crucial separate of geometry as this cognition is extended for the construction of other geometric figures as well, chiefly the triangles. Before talking about constructing angles with a protractor, let us promptly recall angles and their types. An angle is made when two rays start from a park sharpen. This point is called the vertex of the angle and the two rays forming the fish are called its arms or sides. Depending on the inclination between its two arms, an angle may be acute ( less than 90 degrees ), obtuse ( more than 90 degrees ) or right-angled ( precisely 90 degrees ) .
In this article, we will discuss

  • constructing angles of given measure as well as of unknown measure using geometric tools such as the
    • Protractor
    • Compasses
    • Ruler
  • How to construct a 75-degree angle

Also check: Examples of Construction of Different Angles

The Protractor

It is a semi-circular disk used to draw and measure angles. It is graduated from 0 to 180 degrees and can be immediately used to measure any slant within the compass. It has two sets of markings, 0 to 180 degrees from left to right and frailty versa .
Contructing angles - protractor

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Constructing Angles Using a Protractor

For constructing angles of any given measure, be it an acute, an obtuse or a right-angle, the simplest method is by using a protractor. Let us say, you are asked to construct an angle of 120 degrees. The ask steps are :
Step 1: Draw a line segment BC, which is one of the arms of the slant that is to be constructed .
Constructing Angles Using a Protractor - Step 1
Step 2: Place the protractor with its point O on point B of the line segment BC .
Constructing Angles Using a Protractor - Step 2
Step 3: Align OQ along the edge BC .
Step 4: The protractor has bipartisan markings. We consider the scale which has 0 degrees near point C for construction. Mark point A next to the 120 degrees mark on the scale .
Constructing Angles Using a Protractor - Step 3
Step 5: Join points A and B. ∠ABC = 120 degrees is the necessitate angle .
Constructing Angles Using a Protractor - Step 5

Constructing Angles Using Compass

Constructing angles of nameless quantify is basically copying a given lean whose measuring stick is not known. We accomplish this tax using compasses. Let us say that you are given ∠BAC that you are supposed to copy .
Constructing Angles Using Compass
The steps to construct angles using scope are given below :

Step 1: Draw a note PQ. Point P is the vertex of the imitate angle .
Constructing Angles Using Compass - Step 1
Step 2: Place the scope cursor at point A and make an arch that cuts arms AC and AB at points K and J respectively .
Constructing Angles Using Compass - Step 2
Step 3: Without changing the radius of the compass, cut an bow on PQ at point M .
Constructing Angles Using Compass - Step 3
Step 4: Adjust the circumnavigate such that the pointer is placed at K and the pencil promontory at J .
Constructing Angles Using Compass - Step 4
Step 5: With the lapp radius, draw an arch on the first arch with the compass arrow at M. Mark the intersecting point as L .
Constructing Angles Using Compass - Step 5
Step 6: Join the points P and L using a rule. Extend the line up to R .
Constructing Angles Using Compass - Step 6
Step 7: ∠RPQ is the compulsory angle .

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Video Lesson on Constructing Angle

For More Information On Constructing An Angle Of 60 Degrees, Watch The Below Video:

How to Construct 75 degree Angle

To construct a 75-degree angle, we need to produce an fish bisector in between 90-degree angle. Let ’ s learn the steps to construct a 75-degree lean .

  • Step 1: Draw a line segment with endpoint O and A.
  • Step 2: Draw an arc with O as centre cutting the line segment OA at point B with a compass.
  • Step 3: Keeping the radius same, Draw an arc with B as centre cutting the arc at C.
  • Step 4: Keeping the radius same, and C as the center, draw an arc intersecting the arc drawn in the previous step at D.
  • Step 5: With any radius, Draw two arcs with C and D as a center. Intersect these two arcs at E.
  • Step 6: Join OE. angle EOA is the angle with measurement of 90 degrees.
  • Step 7: Now the line OE intersect the arc at the point F.
  • Step 8: Taking F and C as a center, make an arc with a radius of more than half of the measurement FC. The arc intersects at point H.
  • Step 9: Join the point H and O. Angle HOA is the angle obtained of measurement 75 degrees.
  • Step 10: Angle HOA is the desired angle.
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