Angle Relationships in Triangles

Introduction to angle relationships in triangles :

Triangle ,Which is defined as three-sided shape object and with three angles that lies down  in a plane.By adding the three angle in a any triangle,it should be 1800.we can classify the triangles with angles and sides . Angle relationships in triangles, is nothing but we can relate the angles each other for instance,if we have two angles by relating them we can find out another one  .Let us understand angle relationships in triangles with some example.

Types of Triangle
Types of triangle- angle relationships in triangles

Based on side we can classify as

Scalene triangle - having three different length of side
Isosceles triangle - having two equal length of side
Equilateral triangle -three sides are equal


Based on angle we can classify as

Acute triangle-three angles are acute(>900)
Right triangle-One angle should be 900
Obtuse triangle-One angle should be greater than 900(900<α<1800 br="br">[α-angle]

Example to Understand Angle Relationships

Worked example problem- angle relationships in triangles

Equilateral triangle:

Equilateral triangle has all three sides are equal in length and  the three angles also should be same .Three angles are each of 600

Isosceles triangle:

In Isosceles triangle  any two sides should be equal.The angles opposite to the equal side should be same.

Example:

1.Consider the Isosceles triangle the one angle of triangle is 740 . What about the other angles?

Solution:

Step 1:

They have given that one angle of triangle is 740

Step 2:

Since it is Isosceles triangle the two angle should be same.

So     x+x+740=1800

2x+740=1800

2x=180-740

2x=1060

x=530

The angles are 530, 530 , 740

Scalene triangle

Scalene triangle is defined as, it has all three different sides and three angles also should be different.

Right angle triangle:

In a right angle triangle, any one angle must be right angle (angle=900)
In right triangle the side opposite to right angle is longest compare with other sides and it is named as hypotenuse.Is this topic Congruent Polygons Definition hard for you? Watch out for my coming posts.
The other two sides are named as leg.
Triangle properties are related to Pythagorean Theorem


Example:

1. Consider in a right angle triangle the one angle is 670 .Find out the other angles of triangle?

Solution:

Step 1:

They have given that it is right triangle and another one angle is 670

Step 2:

Since it is right angle triangle one angle is 900

The third angle,

900+670+x=1800

1570+x=1800

x = 1800-1570

x=230

The three angles of a triangle are 900,230,670

Acute triangle:

In acute triangles ,the three angles should be less than 900

Example:

1.In Acute triangle the two angles are 590,720. What is the another one angle?

Solution:

Step 1:

Since it is Acute triangle three should be less than 900

590+720 +x=1800

x= 1800-1310

x=490

The three angles of triangles are 490,590, 720

Obtuse triangle:

Obtuse triangle,which has one angle that should be above 900

Example:

1.In obtuse triangle the two angles are 1370,280. What is the another one angle?

Solution:

Step 1:

Since it is obtuse triangle, one should be above 900

1370+280 +x=1800

x= 1800-1650

x=150

The three angles of triangles are 1370,280, 150

Complementary angles:

If the sum up of two angle is 900 then it is called Complementary angles

Supplementary angles:

If the sum up of two angle is 1800 then it is called Supplementary angles

1.If the degree of Complementary angles with numbers are in the ratio of 3:4.Find the biggest angle?

3x+4x=900

7x=900

x=12.850

4x=4(12.850)

Biggest angle=51.40

2.If the degree of Supplementary  angles with numbers are in the ratio of 3:4.Find the biggest angle?

3x+4x=1800

7x=1800

X=25.70

4x=4(25.70)

Biggest angle=102.80