Geometry

Angles In Shape

• Every object around us has a specific shape.
• The shape is classified into two types: Open shape and Closed shape.
• The shape in which the starting and the ending point are not the same is called the open shape. An open shape has space between them.
• The shape in which the starting and the ending point are the same is called the closed shape. A closed shape has no space between them.
  
• A circle is a closed shape.
• A semi-circle is an open shape.
• The angle inside the shape is called the interior angle of a shape.

Angles in a Triangle

• A triangle is three sides bounded figure.
• It has three interior angles.
• Sum of the interior angle of the triangle is 180°.

The three-interior angle of the triangle is ∠A, ∠B, and ∠C. ∠A + ∠B + ∠C = 180°.

Equilateral angle:

A triangle in which all the interior angles are equal to 60° is called an equilateral triangle.

Isosceles angle:

A triangle in which two interior angles are equal is called an isosceles triangle.

Scalene triangle:

A triangle in which no interior angles are equal is called a scalene triangle.

Right-angled triangle:

A triangle in which one of the angles is equal to 90° is called a right-angled triangle.

Angles in a Rectangle

• A rectangle is four sides closed figure.
• Opposite sides of the rectangle are parallel and equal.
• It has 4 interior angles.
• Each interior of the rectangle is equal to 90°.
• Sum of the interior angle of the rectangle is 360°.

The four-interior angle of the rectangle is ∠A, ∠B, ∠C, and ∠D.

∠A = ∠B = ∠C = ∠D = 90°

∠A + ∠B + ∠C + ∠D = 360°

Angles in a Square

• A square is four sides closed figure.
• Each side of the square is equal in length.
• It has 4 interior angles.
• Each interior of the square is equal to 90°.
• Sum of the interior angle of the square is 360°.

The four-interior angles of the square are ∠A, ∠B, ∠C, and ∠D.

∠A = ∠B = ∠C = ∠D = 90°

∠A + ∠B + ∠C + ∠D = 360°

Missing angles

Example 1:

Find the missing angle of the given triangle.

Solution:

Sum of the given angle = 120° + 28°

                 = 148°

The total sum of the interior angle = 180°

Missing angle = 180° – 148°

                 = 32°

Example 2:

Find the missing angle.

Solution:

Given angle = 60°

Total sum = 90°

Missing angle = 90° – 60°

                 = 30°

Did you know?