CLASSIFICATION OF PAIR OF ANGLES

We shall classify a pair of angles in the following way for better understanding and usages.

(i) Two angles that have the exact same measure are called congruent angles.

(ii) Two angles that have their measures adding to 90° are called complementary angles.

(iii) Two angles that have their measures adding to 180° are called supplementary angles.

(iv) Two angles between 0° and 360° are conjugate, if their sum equals 360°.

Example 1 :

In the figure shown below,  let the lines l₁ and l₂ be parallel and t is transversal. Find the value of x.

Solution : 

From the given figure, 

∠(2x + 20)° and ∠(3x - 10)° are corresponding angles. 

So, they are congruent. 

Then, 

2x + 20  =  3x - 10

30  =  x

Example 2 :

In the figure shown below, let the lines l₁ and l₂ be parallel and m is transversal. Identify the pairs of angles which are congruent. 

Example 3 :

Find the value of x :

Solution :

From the picture above, it is clear that the angles (x+1), (x-1) and (x+3) are complementary.  

Then,

(x+1) + (x-1) + (x+3)  =  90

x + 1 + x - 1 + x + 3  =  90

Simplify.

3x + 3  =  90

Subtract 3 from each side. 

3x  =  87

Divide each side by 3.

x  =  29

So, the value of x is 29.

Example 4 :

Find the value of x :

Solution :

From the picture above, it is clear (5x+4), (x-2) and (3x+7) are supplementary angles. 

Then, 

(5x+4) + (x-2) + (3x+7)  =  180

5x + 4 + x -2 + 3x + 7  =  180

Simplify. 

9x + 9  =  180

Subtract 9 from each side.

9x  =  171

Divide each side by 9.

x  =  19

So, the value of x is 19.

Example 5 :

Find the conjugate of the angle measure 97°. 

Solution : 

Let x° be the conjugate of the angle measure 97°. 

Because x° and 97° are conjugate, their sum equals 360°.

Then, 

x° + 97°  =  360°

Subtract 97° from each side. 

x°  =  263°

So, the conjugate of the angle measure 97° is 263°. 

Example 6 :

If (x + 30)° and (2x - 60)° are conjugate, find the value of x.  

Solution : 

Because (x + 30)° and (2x - 60)° are conjugate, their sum equals 360°.

Then, 

(x + 30)° + (2x - 60)°  =  360°

x + 30 + 2x - 60  =  360

Simplify.

3x - 30  =  360

Add 30 to each side. 

3x  =  390

Divide each side by 3.

x  =  130

So, the value of x is 130.

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

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

WORD PROBLEMS

HCF and LCM  word problems

Word problems on simple equations 

Word problems on linear equations 

Word problems on quadratic 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