# EXTERIOR ANGLES AND REMOTE INTERIOR ANGLES WORKSHEET

## About "Exterior angles and remote interior angles worksheet"

Exterior angles and remote interior angles worksheet :

Worksheet given in this section is much useful to the students who would like to practice problems on exterior angle and its two remote interior angles in a triangle.

## Exterior angles and remote interior angles worksheet - Problems

1.  Sketch a triangle and label the exterior angle and its two remote interior angles.

2. Find the relationship between the measure of an exterior angle and the measures of its remote interior angles.

3.  How many exterior angles does a triangle have at each vertex ?

4.  How many total exterior angles does a triangle have ? ## Exterior angles and remote interior angles worksheet - Solution

Problem 1 :

Sketch a triangle and label the exterior angle and its two remote interior angles.

Solution : In the above diagram,

• m∠1, m∠2, and m∠3 are interior angles.
• m∠4 is an exterior angle.
• m∠1 and m∠2 are remote interior angles to m∠4.

Problem 2 :

Find the relationship between the measure of an exterior angle and the measures of its remote interior angles.

Solution :

There is a special relationship between the measure of an exterior angle and the measures of its remote interior angles.

Let us understand this relationship through the following steps.

Step 1 :

Sketch a triangle and label the angles as m∠1, m∠2 and m∠3. Step 2 :

According to Triangle Sum Theorem, we have

m∠1 + m∠2 + m∠3  =  180° ------ (1)

Step 3 :

Extend the base of the triangle and label the exterior angle as m∠4. Step 4 :

m∠3 and m∠4 are the angles on a straight line.

So, we have

m∠3 + m∠4  =  180° ------ (2)

Step 5 :

Use the equations (1) and (2) to complete the following equation,

m∠1 + m∠2 + m∠3  =  m∠3 + m∠4 ------ (3)

Step 6 :

Use properties of equality to simplify the equation (3).

m∠1 + m∠2 + m∠3  =  m∠3 + m∠4

Subtract m∠3 from both sides.

aaaaaaaaaaa m∠1 + m∠2 + m∠3  =  m∠3 + m∠4 aaaaaaaaaaa aaaaaaaaaaaaaaaaaaaaa  - m∠3   - m∠3 aaaaaaaaaaaaaaaaa aaaaaaaaaaa ------------------------------------ aaaaaaaaaaa aaaaaaaaaaa m∠1 + m∠2             =            m∠4 aaaaaaaaaaa aaaaaaaaaaa ------------------------------------ aaaaaaaaaaa

Hence, the Exterior Angle Theorem states that the measure of an exterior angle is equal to the sum of its  remote interior angles.

Problem 3 :

How many exterior angles does a triangle have at each vertex ?

Solution :

Sketch a triangle and draw all of its exterior angles. From the diagram given above, it is clear that each vertex has two exterior angles.

Problem 4 :

How many total exterior angles does a triangle have ?

Solution :

From the diagram given in the above problem 3, it is clear that  a triangle has a total of six exterior angles. After having gone through the stuff given above, we hope that the students would have understood "Exterior angles and remote interior angles worksheet".

Apart from the stuff given above, if you want to know more about "Exterior angles and remote interior angles", 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

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