"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
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.
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!
-
10th Grade Science: Life Processes with Complimentary Ncert Solutions 2023-07-25 00:51:45
Solution: The inner lining of the small intestine undergoes a structural modification, forming villi, which are finger-like projections. These villi serve to increase the surface area for the absorption of digested food. Furthermore, they have a high vascularity, meaning they are well-supplied
-
Creating a Lovely and Simple Homemade Rakhi 2023-07-25 00:50:08
Creating Your Own Homemade RakhiThe glimmer in your eyes and the fervent desires in your heart paint a clear picture: you're filled with ideas for surprising your loved ones on Raksha Bandhan! Are you aware of what that entails? It means that Raksha Bandhan is fast approaching, leaving us with limited
-
10th Grade Science Life Processes: Access Ncert Solutions for Free 2023-07-25 00:03:33
Solution: The inner lining of the small intestine undergoes a transformation into tiny finger-like projections known as villi that enhance the surface area for the absorption of digested food. These villi are abundantly supplied with blood vessels, making them highly vascularized. Additionally,
-
10 Years - Information on Wikipedia 2023-07-24 02:56:26
A decade, which comes from the Ancient Greek word δεκάς (dekas) meaning 'a group of ten', is a span of ten years. Decades can refer to any period of ten years, whether it is someone's lifespan or a specific grouping of calendar years.Usage:Any period of ten years is considered a "decade". For