# CLASSIFYING TRIANGLES BY ANGLES WORKSHEET

Classifying Triangles by Angles Worksheet :

Worksheet given in this section will be much useful for the students who would like to practice problems on classifying triangles by angles.

## Classifying Triangles by Angles Worksheet - Problems

Problem 1 :

Identify the type of triangle whose diagram is given below. Problem 2 :

Identify the type of triangle whose diagram is given below. Problem 3 :

Identify the type of triangle whose diagram is given below. Problem 4 :

Identify the type of triangle whose diagram is given below. Problem 5 :

If (2x + 15)°, (3x)° and (6x)° are the angles of a triangle, identify the type of triangle. ## Classifying Triangles by Angles Worksheet - Solutions

Problem 1 :

Identify the type of triangle whose diagram is given below. Solution :

Let us consider the following two important points related to the given information.

(i)  All the given three angles are different.

(ii)  Each of the three angles is less than 90°

So, the given triangle is a scalene and acute triangle.

Problem 2 :

Identify the type of triangle whose diagram is given below. Solution :

Let us consider the following two important points related to the given information.

(i)  One of the angles is greater than 90°

(ii)  Two sides are equal in length. The angles formed by the two congruent sides with the third side also must be equal.

So, the given triangle is an isosceles and obtuse triangle.

Problem 3 :

Identify the type of triangle whose diagram is given below. Solution :

In the triangle above, the lengths of all the three sides are same and all the three angles are congruent.

So, the given triangle is equiangular triangle.

Problem 4 :

Identify the type of triangle whose diagram is given below. Solution :

In the triangle above, two sides are congruent. The angles formed by the third side with two congruent sides will always be equal.

The diagram given below illustrates this. By Triangle Sum theorem, we have

x + x + 40°  =  180°

2x + 40°  =  180°

Subtract 40° from both sides.

2x  =  140°

Divide both sides by 2.

x  =  70°

The angles measures of the given triangle are 40°, 70° and 70°.

Let us consider the following two important points from the above calculation.

(i)  Two of the angles are equal

(ii)  Each of the three angles is less than 90°.

From the above two points, we have

The given triangle is an isosceles and acute triangle.

Problem 5 :

If (2x + 15)°, (3x)° and (6x)° are the angles of a triangle, identify the type of triangle.

Solution:

The angle sum property of a triangle states that the angles of a triangle always add up to 180°.

Then,

(2x + 15)° + (3x)° + (6x)°  =  180°

2x + 15 + 3x + 6x  =  180

Simplify.

11x + 15  =  180

Subtract 15 from each side.

11x  =  165

Divide each side by 11.

x  =  15

Substitute 15 for x into the given expressions to find the angles of the triangle.

First angle  =  2x + 15  =  2(15) + 15  =  45°

Second angle  =  3x  =  3(15)  =  45°

Third angle  =  6x  =  6(15)  =  90°

Let us consider the following two important points from the above calculation.

(i)  Two of the angles are equal

(ii)  One of the angles is 90°

So, the given triangle is an isosceles and right triangle. After having gone through the stuff given above, we hope that the students would have understood how to classify triangles by angles.

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 