# CONSTRUCTION OF ANGLES USING RULER AND COMPASS

Construction of Angles Using Ruler and Compass :

In this section, you will learn how to construct angles using ruler and compass.

To construct an angle, we must need the following mathematical instruments.

1. Ruler

2. Compass

## Constructing Angles Using Ruler and Compass - Examples

Example 1 :

Construct an acute angle of 60°.

Step 1 :

Draw a line ‘l’ and mark a point ‘O’ on it. Step 2 :

(i) With ‘O’ as center draw an arc of any radius to cut the line at A.

(ii) With the same radius and A as center draw an arc to cut the previous arc at B. Step 3 :

(i) Join OB.

(ii) We get the required angle AOB = 60°. Example 2 :

Construct an acute angle of 30°.

Step 1 :

(i) First let us construct 60° angle and then bisect it to get 30° angle.

(ii) Construct 60° (as shown in the above example). Step 2 :

(i) With ‘A’ as center, draw an arc of radius more than half of AB in the interior of AOB.

(ii) With the same radius and with B as center draw an arc to cut the previous one at C.

(iii) Join OC.

(iv) We get the required angle AOC  =  30°. Example 3 :

Construct an obtuse angle of 120°.

Step 1 :

Draw a line ‘l’ and mark a point ‘O’ on it. Step 2 :

With ‘O’ as center draw an arc of any radius to cut the line l at A. Step 3 :

(i)  With same radius and with ‘A’ as center draw another arc to cut the previous arc at ‘B’.

(ii)  With ‘B’ as center draw another arc of same radius to cut the first arc at ‘C’. Step 4 :

(i)  Join OC.

(ii)  We get the required angle AOC  =  120°. Example 4 :

Construct a right angle  90°.

Step 1 :

(i)  To construct 90° angle, we are going to bisect the straight angle 180°.

(ii)  Mark a point ‘O’ on a straight line ‘l’. Step 2 :

(i)  With ‘O’ as center draw arcs of any radius to cut the line l at A and B.

(ii)  Now AOB  =  180°. Step 3 :

With A and B as centers and with the radius more than half of AB draw arcs above AB to intersect each other at ‘C’. Step 4 :

(i)  Join OC.

(ii)  We get the required angle AOC  =  90°.  Apart from using ruler and compass, we can construct angles using ruler and protractor also.

To know how to construct angles using ruler and protractor,

After having gone through the stuff given above, we hope that the students would have understood how to construct angles using ruler and compass.

Apart from the stuff given in this section, if you need any other stuff in math, please use our google custom search here.

You can also visit our following web pages on different stuff in math.

WORD PROBLEMS

Word problems on simple equations

Word problems on linear equations

Algebra word problems

Word problems on trains

Area and perimeter word problems

Word problems on direct variation and inverse variation

Word problems on unit price

Word problems on unit rate

Word problems on comparing rates

Converting customary units word problems

Converting metric units word problems

Word problems on simple interest

Word problems on compound interest

Word problems on types of angles

Complementary and supplementary angles word problems

Double facts word problems

Trigonometry word problems

Percentage word problems

Profit and loss word problems

Markup and markdown word problems

Decimal word problems

Word problems on fractions

Word problems on mixed fractrions

One step equation word problems

Linear inequalities word problems

Ratio and proportion word problems

Time and work word problems

Word problems on sets and venn diagrams

Word problems on ages

Pythagorean theorem word problems

Percent of a number word problems

Word problems on constant speed

Word problems on average speed

Word problems on sum of the angles of a triangle is 180 degree

OTHER TOPICS

Profit and loss shortcuts

Percentage shortcuts

Times table shortcuts

Time, speed and distance shortcuts

Ratio and proportion shortcuts

Domain and range of rational functions

Domain and range of rational functions with holes

Graphing rational functions

Graphing rational functions with holes

Converting repeating decimals in to fractions

Decimal representation of rational numbers

Finding square root using long division

L.C.M method to solve time and work problems

Translating the word problems in to algebraic expressions

Remainder when 2 power 256 is divided by 17

Remainder when 17 power 23 is divided by 16

Sum of all three digit numbers divisible by 6

Sum of all three digit numbers divisible by 7

Sum of all three digit numbers divisible by 8

Sum of all three digit numbers formed using 1, 3, 4

Sum of all three four digit numbers formed with non zero digits

Sum of all three four digit numbers formed using 0, 1, 2, 3

Sum of all three four digit numbers formed using 1, 2, 5, 6 