"Master the Art of Angle Construction with a Compass"

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1. Create a 60° Angle with a Compass

Step-by-Step:

• (i) Begin by drawing a ray OA.
• (ii) Using O as the center and a suitable radius, draw an arc above OA to intersect at point B.
• (iii) Next, using B as the center and the same radius, draw an arc intersecting the previous arc at point C.
• (iv) Connect points OC and extend it to point D.
• The resulting angle, ∠AOD, will measure 60°.

• 2. Build a 120° Angle using a Compass

• Step-by-Step:
• (i) Start by drawing a ray OA.
• (ii) Using O as the center and any convenient radius, draw an arc intersecting OA at point B.

(iii) Using B as the center and the same radius, draw an arc intersecting at point C. Then, using C as the center and the same radius, cut the arc again at point D.

(iv) Join points OD and extend it to point E.

The resulting angle, ∠AOE, will measure 120°.

3. Build a 30° Angle using a Compass and a Bisector

Step-by-Step:

• (i) First, construct an angle ∠AOD measuring 60° as shown.
• (ii) Draw the bisector OE of ∠AOD.
• The resulting angle, ∠AOD, will be bisected to measure 30°.

• 4. Create a 90° Angle through Compass Constructions

• Step-by-Step:
• (i) Begin by selecting any ray OA.
• (ii) Using O as the center and any convenient radius, draw an arc intersecting OA at point B.
• (iii) Using B as the center and the same radius, draw an arc intersecting the first arc at point C.
• (iv) Using C as the center and the same radius, cut the first arc again to intersect at point D.

(v) Using C and D as the centers and a radius longer than half of CD, draw two arcs that will intersect at point E. Join OE.

The resulting angle, ∠EOA, will measure 90°.

5. Construct a 90° Angle through Complex Compass and Ruler Constructions

Step-by-Step:

• (i) First, select a ray OA.
• (ii) Using O as the center and any suitable radius, draw an arc intersecting OA at point C.
• (iii) Using C as the center and the same radius, draw an arc intersecting the first arc at point M.
• (iv) Using M as the center and the same radius, cut the first arc again at point L.

(v) Using L and M as the centers and a radius longer than half of LM, draw two arcs that will intersect at point B. Join OB, which will form a 90° angle.

(vi) Using N and M as the centers, draw two additional intersecting arcs at point P.

The resulting angle, ∠OBP, will measure 90°.

To construct this shape, follow these specific steps using the specified geometric techniques and measurements.

(i) Begin by creating a 90° angle using point P as a reference. Then, use centers L and N to draw two intersecting arcs that meet at point S.

(ii) Join points S and O to form line SO which creates a new angle. This angle measures 105° and is denoted by ∠SOA.

(i) To create the next angle, construct ∠AOD measuring a perfect 90°.

(ii) Extend line segment AO to point B.

(iii) Proceed to draw a line from point O to point E that bisects angle ∠DOB, forming a new 45° angle represented by ∠DOE.

With this new angle, it is evident that ∠EOA = 45° + 90° = 135°.

(i) To construct the final angle in this series, begin by constructing a 120° angle at point A.

(ii) Extend line segment AO to point B.

(iii) Draw a line from point O to point D which bisects angle COB.

At this point, the angle ∠COD will measure 30°. Through some simple calculations, we can determine that ∠AOD measures 150°.

Additional resources about angles, such as their types, measurements, and techniques for bisecting them, can be found through the links below:

● Angles.

Interior and Exterior Angles.

Angle Measurement using a Protractor.

Different Types of Angles.

Angle Pairs.

Bisecting Angles.

Explore the world of angles with our helpful resources! Discover the art of constructing angles using a trusty compass with our Angle Construction Guide. For additional practice, check out our Angle Worksheet or challenge yourself with our Geometry Practice Test.

If you're a 5th grader looking to up your geometry game, we've got you covered. Take a peek at our 5th Grade Geometry Page or tackle some tough 5th Grade Math Problems.

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