"Master the Art of Angle Construction with a Compass"
Discover the art of constructing angles using a compass and a ruler with expert precision, while preserving the ,
, , tag structure.1. Create a 60° Angle with a Compass
StepbyStep:
 (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
 StepbyStep:
 (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
StepbyStep:
 (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
 StepbyStep:
 (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
StepbyStep:
 (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.
Still didn't find what you were looking for? Don't sweat it! Head on over to our homepage and use the handy Google Search tool to explore the endless possibilities of Math Only Math. And don't forget to share this page with your friends using the links below!
1. Create a 60° Angle with a Compass
StepbyStep:
 (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
 StepbyStep:
 (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
StepbyStep:
 (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
 StepbyStep:
 (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
StepbyStep:
 (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.
Still didn't find what you were looking for? Don't sweat it! Head on over to our homepage and use the handy Google Search tool to explore the endless possibilities of Math Only Math. And don't forget to share this page with your friends using the links below!

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