how to draw 75 degree angle with compass

Before talking about building angles with a protractor, let’s quickly recall angles and their forms. An angle is created when two rays start from a common point. This point is called the vertex of the angle and the two rays that form the angle are called its arms or sides. Depending on the tilt between its arms, an angle can be acute (less than 90 degrees), obtuse (more than 90 degrees), or right angles (exactly 90 degrees). Angle construction is an important part of geometry as this knowledge is extended to construct other geometric figures, mainly triangles.

  • construct angles of given measure as well as of unknown measure using geometry tools like
  • How to create a 75 degree angle

ProtractorsIt is a semicircular disk used for drawing and measuring angles. It is graduated from 0 to 180 degrees and can be used directly to measure any angle in the range. It has two sets of markers, 0 to 180 degrees from left to right and vice versa.Construct angles with a protractorTo construct angles of any given measure, be it acute, obtuse or right angle, the simplest method is to use a protractor. Let’s say you are asked to make a 120 degree angle. The required steps are:

  • Draw the line segment BC, which is one of the branches of the vertical angle.

Read more: How to troubleshoot an uncomfortable situationBuilding angles with a protractor - Step 1

  • Place the protractor with point O on point B of line segment BC.

Building angles with a protractor - Step 2

  • Let OQ along side BC.
  • Protractor with two-way markings. We consider the scale to have 0 degrees near point C for construction. Mark point A next to the 120 degree mark on the scale.
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Building angles with a protractor - step 4

  • Join the points A and B. ∠ABC = 120 degrees is the required angle.

Building angles with a protractor - Step 5Undefined measuring angle constructionConstructing angles of unknown measure is essentially duplicating a given angle of unknown measure. We complete this task using the compass. Let us say that you are given a ∠BAC that you must copy.Undefined measuring angle constructionThe steps are:

  • Draw the line PQ. Point P is the vertex of the copy angle.

Read more: How to add luna to keplr . walletConstructing Unknown Protractor Angles - Step 1

  • Place the compass pointer at point A and make an arc that cuts the AC and AB branches at points K and J respectively.

Constructing an unknown measuring angle - step 2

  • Without changing the radius of the compass, cut an arc on PQ at point M.

Constructing Unknown Protractor Angles - Step 3

  • Adjust the compass so that the pointer is at K and the tip of the pencil is at J.

Constructing an unknown measuring angle - step 4

  • With the same radius, draw an arc on the first arc with the compass pointer at M. Mark the intersection as L.

Constructing an unknown measuring angle - step 5

  • Connect the points P and L with a ruler. Extend the line up to R.

Unknown measuring angle construction - step 6

  • ∠RPQ is the required angle.

For more information on how to build a 60 degree angle, watch the video below:

How to create a 75 degree angle

To create a 75 degree angle, we need to create a bisector in the middle of the 90 degree angle. Let’s learn the steps to build a 75 degree angle.

  • Step 1: Draw a line segment with endpoints O and A.
  • Step 2: Draw an arc with center O intersecting line segment OA at point B with compass.
  • Step 3: Keeping the radius, Draw an arc with B as the center of the arc at C.
  • Step 4: Keeping the radius and C as the center, draw an arc that intersects the arc drawn in the previous step at D.
  • Step 5: With any radius, Draw two arcs with C and D as centers. The intersection of these two arcs is at E.
  • Step 6: Join OE. Angle EOA is an angle that measures 90 degrees.
  • Step 7: Now the line OE intersects the chord at point F.
  • Step 8: Using F and C as centers, construct an arc with radius half the measure FC. The chords intersect at point H.
  • Step 9: Connect the points H and O. Angle HOA is an angle that measures 75 degrees.
  • Step 10: The HOA angle is the desired angle.
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To learn more about building corners, download BYJU’S – Learning App. Read more: How to build bubbling ice trait

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