# ANGLE RELATIONSHIPS

Angle relationships :

It is useful to work with pairs of angles and to understand how pairs of angles relate to each other.

## Different types of angle relationships

Congruent angles :

Congruent angles are angles that have the same measure.

Vertical angles :

Vertical angles have a common vertex, but they are never adjacent angles. And also, vertical angles are always congruent.

Complementary angles :

If the sum of two angles is 90⁰, then those two angles are called as complementary angles.

Supplementary angles :

If the sum of two angles is 180⁰, then those two angles are called as supplementary angles.

Adjacent angles are two angles that have a common vertex and a common side.

## Angle relationships - Practice questions

Question 1 :

Find the value of  "x" in the figure given below.

Solution :

From the picture above, it is very clear that the angles "x" and "2x" are complementary.

So, we have x + 2x = 90°

3x  =  90°

x  =  30°

Hence the value of "x" is 30°.

Question 2 :

Find the value of  "x" in the figure given below.

Solution :

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

So, we have (x+1) + (x-1) + (x+3) = 90

3x + 3  =  90

3x  =  87

x  =  29

Hence the value of "x" is 29.

Question 3 :

Find the value of  "x" in the figure given below.

Solution :

From the picture above, it is very clear that (2x+3) and (x-6) are  supplementary angles.

So, we have (2x+3) + (x-6)  = 180°

2x + 3 + x - 6  =  180°

3x - 3  =  180

3x  =  183

x  =  61

Hence the value of "x" is 61.

Question 4 :

Find the value of  "x" in the figure given below.

Solution :

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

So, we have (5x+4) + (x-2) + (3x+7) = 180°

5x + 4 + x -2 + 3x + 7  =  180°

9x + 9  =  180

9x  =  171

x  =  19

Hence the value of "x" is 19

Question 5 :

Find the value of  "x" in the figure given below.

Solution :

From the picture above, it is very clear (3x+7)° and 100° are vertical angles and also they are congruent.

So, we have (3x + 7)  =  100°

3x  =  93°

x  =  31

Hence the value of "x" is 31.

After having gone through the stuff given above, we hope that the students would have understood "Relationships between angles".

Apart from the stuff given on "How to measure an angle with protractor", if you need any other stuff in math, please use our google custom search here.

WORD PROBLEMS

HCF and LCM  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