**Properties of Triangle 3 :**

This is the continuity of our web content given on "Properties of Triangle 2".

The following are the two important properties of triangle.

1. The sum of the lengths of any two sides of a triangle is greater than the third side.

2. The sum of all the three angles of a triangle is 180°.

1. In an equilateral triangle, all the three sides and three angles will be equal and each angle will measure 60°.

2. In an isosceles triangle, the lengths of two of the sides will be equal. And the corresponding angles of the equal sides will be equal.

2. In a right triangle, square of the hypotenuse is equal to the sum of the squares of other two sides. This is known as Pythagorean theorem.

**Hypotenuse :**

The longest side of in the right triangle which is opposite to right angle (90°)

**Problem 1 : **

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,

x + 1 = 28 + 1 = 29°

2x + 5 = 2(28) + 5 = 56 + 5 = 61°

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

**Problem 2 : **

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.

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°

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

**Problem 3 : **

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 :**

From the given ratio,

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°

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

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