# SUM OF THE ANGLES OF A TRIANGLE WORKSHEET

Problem 1 :

Can 30°, 60° and 90° be the angles of a triangle ?

Problem 2 :

Can 35°, 55° and 95° be the angles of a triangle ?

Problem 3 :

In a triangle, If the second angle is 5° greater than the first angle and the third angle is 5° greater than second angle, find the three angles of the triangle.

Problem 4 :

If the angles of a triangle are in the ratio 2 : 7 : 11, then find the angles.

Problem 5 :

In a triangle, If the second angle is 20% more than the first angle and the third angle is 20% less than the first angle, then find the three angles of the triangle.

Problem 6 :

If 3 consecutive positive integers be the angles of a triangle, then find the three angles of the triangle.

Problem 7 :

In a triangle, if the second angle is 2 times the first angle and the third angle is 3 times the first angle, find the angles of the triangle.

Problem 8 :

In a right triangle, apart from the right angle, the other two angles are x + 1 and 2x + 5. find the angles of the triangle.

Problem 9 :

In a triangle, if the second angle is 3 times the sum of the first angle and 3 and the third angle is the sum of 2 times the first angle and 3, find the three angles of the triangle.

Problem 10 :

In a triangle, the ratio between the first and second angle is 1 : 2 and the third angle is 72. Find the first and second angle of the triangle.

Problem 11 :

The first angle of a triangle is two-third of the third angle, the second angle is double the first angle. Find the three angles of the triangle.

Problem 12 :

In a triangle, sum of the first and second angles is 95°, sum of the second and third angles is 130° and sum of the first and third angles is 135°. Find the three angles of the triangle. Problem 1 :

Can 30°, 60° and 90° be the angles of a triangle ?

Solution :

Let us add all the three given angles and check whether the sum is equal to 180°.

30° +  60° + 90°  =  180°

Because the sum of the angles is equal 180°, the given three angles can be the angles of a triangle.

Problem 2 :

Can 35°, 55° and 95° be the angles of a triangle ?

Solution :

Let us add all the three given angles and check whether the sum is equal to 180°.

35° +  55° + 95°  =  185°

Because the sum of the angles is not equal 180°, the given three angles can not be the angles of a triangle.

Problem 3 :

In a triangle, If the second angle is 5° greater than the first angle and the third angle is 5° greater than second angle, find the three angles of the triangle.

Solution :

Let x be the first angle.

Then, the second angle  =  x + 5

The third angle  =  x + 5 + 5  =  x + 10

We know that,

the sum of the three angles of a triangle  =  180°

x + (x + 5) + (x + 10)  =  180°

3x + 15  =  180

3x  =  165

x  =  55

The first angle  =  55°

The second angle  =  55 + 5  =  60°

The third angle  =  60 + 5  =  65°

So, the three angles of a triangle are 55°, 60° and 65°.

Problem 4 :

If the angles of a triangle are in the ratio 2 : 7 : 11, then find the angles.

Solution :

The angles of the triangle are in the ratio 2 : 7 : 11.

Then, the three angles are

2x, 7x and 11x

In any triangle,

Sum of the three angles  =  180°

So, we have

2x + 7x + 11x  =  180°

20x  =  180

x  =  9

Then, the first angle  =  2x  =  2 ⋅ 9  = 18°

The second angle  =  7x  =  7 ⋅ 9  =  63°

The third angle  =  11x  =  11 ⋅ 9  =  99°

So, the angles of the triangle are 18°, 63° and 99°.

Problem 5 :

In a triangle, If the second angle is 20% more than the first angle and the third angle is 20% less than the first angle, then find the three angles of the triangle.

Solution :

Let x be the first angle.

Then, the second angle  =  120% of x  =  1.2x

The third angle  =  80% of x  =  0.8x

We know that,

the sum of the three angles of a triangle  =  180°

x + 1.2x + 0.8x  =  180°

3x  =  180°

x  =  60°

The first angle  =  60°

The second angle  =  1.2(60)  =  72°

The third angle  =  0.8(60)  =  48°

So, the three angles of a triangle are 60°, 72° and 48°.

Problem 6 :

If 3 consecutive positive integers be the angles of a triangle, then find the three angles of the triangle.

Solution :

Let x be the first angle.

Then, the second angle  =  x + 1

The third angle  =  x + 2

We know that,

the sum of the three angles of a triangle  =  180°

x + x + 1 + x + 2  =  180°

3x + 3  =  180°

3x  =  177°

x  =  59°

The first angle  =  59°

The second angle  =  59 + 1  =  60°

The third angle  =  59 + 2  =  61°

So, the three angles of a triangle are 59°, 60° and 61°.

Problem 7 :

In a triangle, if the second angle is 2 times the first angle and the third angle is 3 times the first angle, find the angles of the triangle.

Solution :

Let x be the first angle.

Then the second angle  =  2x

The third angle  =  3x

We know that,

the sum of the three angles of a triangle  =  180°

x + 2x + 3x  =  180°

6x  =  180°

x  =  30°

The first angle  =  30°

The second angle  =  2 ⋅ 30°  =  60°

The third angle  =  3 ⋅ 30°  =  90°

So, the three angles of a triangle are 30°, 60° and 90°.

Problem 8 :

In a right triangle, apart from the right angle, the other two angles are x + 1 and 2x + 5. find the angles of the triangle.

Solution :

We know that,

the sum of the three angles of a triangle  =  180°

90 + (x + 1) + (2x + 5)  =  180°

3x + 6  =  90°

3x  =  84°

x  =  28°

So, we have

x + 1  =  28 + 1  =  29°

2x + 5  =  2 ⋅ 28 + 5  =  56 + 5  =  61°

So, the three angles of a triangle are 90°, 29° and 61°.

Problem 9 :

In a triangle, if the second angle is 3 times the sum of the first angle and 3 and the third angle is the sum of 2 times the first angle and 3, find the three angles of the triangle.

Solution :

Let x be the first angle.

Then, the second angle  =  3(x + 3)

The third angle  =  2x + 3

We know that,

the sum of the three angles of a triangle  =  180°

x + 3(x + 3) + 2x + 3  =  180°

x + 3x + 9 + 2x + 3  =  180°

6x + 12  =  180°

6x  =  168°

x  =  28°

The first angle  =  28°

The second angle  =  3(28 + 3)  =  93°

The third angle  =  2 ⋅ 28 + 3  =  59°

So, the three angles of a triangle are 28°, 93° and 59°.

Problem 10 :

In a triangle, the ratio between the first and second angle is 1 : 2 and the third angle is 72. Find the first and second angle of the triangle.

Solution :

The ratio of the first angle and second angle is 1 : 2.

Then, the first angle  =  x

The second angle  =  2x

We know that,

the sum of the three angles of a triangle  =  180°

x + 2x + 72  =  180°

3x  =  108°

x  =  36°

The first angle  =  36°

The second angle  =  2 ⋅ 36°  =  72°

So, the first angle is  36° and the second angle is 72°.

Problem 11 :

The first angle of a triangle is two-third of the third angle, the second angle is double the first angle. Find the three angles of the triangle.

Solution :

Let x be the third angle.

Then, the first angle is

=  2x/3

Second angle is

=  2 ⋅ 2x/3

=  4x/3

We know that,

the sum of the three angles of a triangle  =  180°

Then,

x + 2x/3 + 4x/3  =  180°

3x/3 + 2x/3 + 4x/3  =  180°

(3x + 2x + 4x) / 3  =  180°

9x / 3  =  180°

3x  =  180°

Divide each side by 3.

x  =  60°

That is,

the third angle  =  60°

Then,

the first angle  =  2x/3  =  2(60°) / 3  =  40°

the second angle  =  4x/3  =  4(60°) / 3  =  80°

So, the three angles of the triangle are 40°, 80° and 60°.

Problem 12 :

In a triangle, sum of the first and second angles is 95°, sum of the second and third angles is 130° and sum of the first and third angles is 135°. Find the three angles of the triangle.

Solution :

Let x, y and z be the first, second and third angles of the  triangle respectively.

From the given information, we have

x + y  =  95° -----(1)

y + z  =  130° -----(2)

x + z  =  135° -----(3)

Add (1), (2) and (3) :

2x + 2y + 2z  =  360°

2(x + y + z)  =  360°

Divide each side by 2.

x + y + z  =  180°

Substitute 95° for 'x + y' [from (1)].

95° + z  =  180°

z  =  85°

Substitute z  =  85° in (2).

y + 85°  =  130°

y  =  45°

Substitute y  =  45° in (1).

x + 45°  =  95°

x  =  50°

So, the three angles of the triangle are 50°, 45° and 85°. 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

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 