**Angle pair relationships worksheets :**

Worksheet given in this section is much useful to the students who would like to practice problems on different relationships between pairs of angles.

**Problem 1 :**

Look at the picture shown below and answer the following questions.

(i) Are m∠2 and m∠3 a linear pair ?

(ii) Are m∠3 and m∠4 a linear pair ?

(iii) Are m∠1 and m∠3 vertical angles ?

(iv) Are m∠2 and m∠4 vertical angles ?

**Problem 2 :**

In the stair railing shown at the right, m∠6 has a measure of 130°. Find the measures of the other three angles.

**Problem 3 :**

In the diagram shown below, Solve for "x" and "y". Then, find the angle measures.

**Problem 1 :**

Look at the picture shown below and answer the following questions.

(i) Are m∠2 and m∠3 a linear pair ?

(ii) Are m∠3 and m∠4 a linear pair ?

(iii) Are m∠1 and m∠3 vertical angles ?

(iv) Are m∠2 and m∠4 vertical angles ?

**Solution : **

**Solution (i) : **

No. The angles are adjacent but their non-common sides are not opposite rays.

**Solution (ii) : **

Yes. The angles are adjacent and their non-common sides are opposite rays.

**Solution (iii) : **

No. The sides of the angles do not form two pairs of opposite rays.

**Solution (iv) : **

No. The sides of the angles do not form two pairs of opposite rays.

**Problem 2 :**

In the stair railing shown at the right, m∠6 has a measure of 130°. Find the measures of the other three angles.

**Solution : **

m∠6 and m∠7 are a linear pair. So, the sum of their measures is 180°.

m∠6 + m∠7 = 180°

Substitute m∠6 = 130°

130° + m∠7 = 180°

Subtract 130° from both sides.

m∠7 = 50°

m∠6 and m∠5 are also a linear pair. So, it follows that m∠7 = 50°.

m∠6 and m∠8 are vertical angles. So, they are congruent and they have same measure.

m∠8 = m∠6 = 130°

**Problem 3 :**

In the diagram shown below, Solve for "x" and "y". Then, find the angle measures.

**Solution : **

Use the fact that the sum of the measures of angles that form a linear pair is 180°.

**Solving for "x" :**

m∠AED and m∠DEB are a linear pair. So, the sum of their measures is 180°.

m∠AED + m∠DEB = 180°

Substitute m∠AED = (3x+5)° and m∠DEB = (x+15)°.

(3x+5)° + (x+15)° = 180°

Simplify.

4x + 20 = 180

Subtract 20 from both sides.

4x = 160

Divide both sides by 4.

x = 40

**Solving for "y" :**

m∠AEC and m∠CEB are a linear pair. So, the sum of their measures is 180°.

m∠AEC + m∠CEB = 180°

Substitute m∠AEC = (y+20)° and m∠CEB = (4y-15)°.

(y+20)° + (4y-15)° = 180°

Simplify.

5y + 5 = 180

Subtract 5 from both sides.

5y = 175

Divide both sides by 5.

y = 35

**Use substitution to find the angle measures :**

m∠AED = (3x + 5)° = (3 • 40 + 5)° = 125°

m∠DEB = (x + 15)° = (40 + 15)° = 55°

m∠AEC = ( y + 20)° = (35 + 20)° = 55°

m∠CEB = (4y º 15)° = (4 • 35 º 15)° = 125°

So, the angle measures are 125°, 55°, 55°, and 125°. Because the vertical angles are congruent, the result is reasonable.

After having gone through the stuff given above, we hope that the students would have understood "Angle pair relationships worksheets".

Apart from the stuff given above, if you want to know more about "Angle pair relationships", please click here

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

HTML Comment Box is loading comments...

**WORD PROBLEMS**

**HCF and LCM word problems**

**Word problems on simple equations **

**Word problems on linear equations **

**Word problems on quadratic equations**

**Area and perimeter word problems**

**Word problems on direct variation and inverse variation **

**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**

**Markup and markdown word problems **

**Word problems on mixed fractrions**

**One step equation word problems**

**Linear inequalities word problems**

**Ratio and proportion word problems**

**Word problems on sets and venn diagrams**

**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 **

**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 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**