 A triangle is a type of polygon that has three sides, angles, vertices. The point where two sides intersect is called vertex and an angle is formed between two sides. The important properties of angles of triangle detail are included here for the convenience of the students. As a part of learning geometry and measurement, you can get the complete details of triangle properties on this page.

Properties of Angles of a Triangle

Based on the angle, triangles are divided into three types. They are acute, obtuse and right triangles. The complete details of important the properties of angles of a triangle are along the lines:

Property 1: Triangle Sum Theorem

The sum of three angles in a triangle is equal to 180°.
Example: ∠A + ∠B + ∠C = 180°

Property 2:

The sum of the interior angle and its adjacent exterior angle is 180°.
Example: Here, b is the interior angle and d is the exterior angle.
b + d = 180°

Property 3:

The side opposite the greater angle is the longest side of all the three sides of a triangle.
Example: The longest angle is ∠A. So, the longest side is BC.

Property 4: Exterior Angle Theorem

The exterior angle of the triangle is equal to the sum of the two opposite interior angles.
Example: Here, d is the exterior angle and a, c are opposite interior angles.
d = a + c.

Property 5:

• An equilateral triangle has 3 equal angles that are 60° each.
• An isosceles triangle has 2 equal angles, which are the angles opposite the 2 equal sides.

Triangle Properties

Every triangle will have the following properties.

• The sum of the angles of a triangle is equal to 180 degrees.
• The sum of lengths of any two sides is more than the length of the third side of the triangle.
• The opposite side of the greater angle is the longest side of all three sides of a triangle.
• The triangles are said to be similar if their corresponding angles are congruent and lengths are proportional.
• The area of a triangle = 1/2 x base x height.
• The perimeter of a triangle is the sum of all its sides.

Solved Questions on Properties of Angles of a Triangle

Question 1: Find the values of x, y.

Solution:
As per the Exterior Angle Theorem, the sum of the interior angle and its adjacent angle is 180 degrees.
So, x° + 104°= 180°
x°= 180 – 104 = 76°
According to Triangle Sum Theorem, the sum of angles is 180 degrees.
x° + y° + 40°= 180°
76° + y°+ 40°= 180°
y° = 64°
Therefore, x = 76°, y = 64°.

Question 2: Find the value of the unknown angle.

Solution:
As per Triangle Sum Theorem, the sum of angles is 180 degrees.
x° + 110° + 30°= 180°
x° = 180 – 140
x° = 40°

Question 3:
In △ABC, if the base is 15 cm, the height is 20 cm. Find its area?

Solution:
Given that,
Base = 15 cm
Height = 20 cm
Area  of the traingle = 1/2 x base x height
= 1/2 x 15 x 20
= 150 cm²
Therefore, triangle area is 150 cm².

1. What are the two properties of triangles?

• The difference between the two sides of a triangle is less than the length of the third side.
• The side opposite the greater angle is the longest side of all the three sides of a triangle.

2. What are the properties of angles in a triangle?

• The sum of the interior angles in a triangle is 180 degrees.
• The sum of the angle and its adjacent exterior angle of a triangle is 180 degrees.
• The exterior angle is the sum of the opposite interior angles.

3. What is the area and perimeter of the triangle?

The area of the triangle is the region occupied by the triangle and the perimeter is the length of the outer boundary.

4. How many types of triangles are there in Maths?

Basically, there are six types of triangles. They are Equilateral Triangle, Scalene Triangle, Isosceles Triangle, Acute Triangle, Obtuse Triangle and Right Triangle.