In any triangle,

**Sum of the three angles = 180°**

More clearly,

If the sum of the three angles is not equal to 180°, then we can conclude that the three angles can not be the angles of a triangle.

**Example 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.

**Example 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.

**Example 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°.

**Example 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°.

**Example 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°.

**Example 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°.

**Example 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°.

**Example 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°.

**Example 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°.

**Example 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°.

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

HTML Comment Box is loading comments...

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 **

**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**

**Trigonometry 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**