krit.club logo

Shapes and Angles - Angles in Shapes and Names

Grade 5CBSE

Review the key concepts, formulae, and examples before starting your quiz.

🔑Concepts

•

An angle is formed when two rays or line segments meet at a common endpoint called the vertex. Visually, you can think of an angle as the space or 'opening' between two fingers when you spread them apart.

•

A Right Angle measures exactly 90∘90^{\circ}. It looks like a perfect 'L' shape or the corner of a square. When you see a small square symbol in a corner, it indicates a right angle.

•

An Acute Angle is any angle that measures more than 0∘0^{\circ} but less than 90∘90^{\circ}. Visually, it is 'sharper' and narrower than a right angle, similar to the tip of a pencil or a slice of pizza.

•

An Obtuse Angle is an angle that measures more than 90∘90^{\circ} but less than 180∘180^{\circ}. It appears 'blunt' and wide, like the hands of a clock showing 4 o'clock or an open laptop screen tilted back.

•

A Straight Angle measures exactly 180∘180^{\circ}. It looks like a perfectly straight line. You can imagine two rays pointing in opposite directions from the same vertex to create this flat appearance.

•

Shapes are defined by their number of sides and angles. For example, a triangle has 3 sides and 3 angles, while a quadrilateral (like a square or rectangle) has 4 sides and 4 angles. If you change the angles of a shape without changing the side lengths, the name of the shape can change (e.g., a square becoming a rhombus).

•

Angles are measured in degrees using a tool called a protractor. A protractor is a semi-circular device with markings from 0∘0^{\circ} to 180∘180^{\circ}. To measure an angle, place the center point of the protractor on the vertex and align the zero line with one side of the angle.

📐Formulae

Sum of interior angles of a triangle = 180∘180^{\circ}

Sum of interior angles of a quadrilateral = 360∘360^{\circ}

Sum of interior angles of a polygon with nn sides = (n−2)×180∘(n - 2) \times 180^{\circ}

💡Examples

Problem 1:

In a triangle, two angles are 45∘45^{\circ} and 75∘75^{\circ}. Find the measure of the third angle.

Solution:

Step 1: Add the known angles: 45∘+75∘=120∘45^{\circ} + 75^{\circ} = 120^{\circ}.\nStep 2: We know the sum of all angles in a triangle is 180∘180^{\circ}.\nStep 3: Subtract the sum of the known angles from 180∘180^{\circ}: 180∘−120∘=60∘180^{\circ} - 120^{\circ} = 60^{\circ}.

Explanation:

Since the total sum of angles in any triangle must be 180∘180^{\circ}, we find the missing value by subtracting the known parts from the total.

Problem 2:

A shape has four internal angles. Three of the angles are 90∘90^{\circ} each. What is the value of the fourth angle, and what type of angle is it?

Solution:

Step 1: Identify the shape as a quadrilateral since it has 4 angles.\nStep 2: Calculate the sum of the three known angles: 90∘+90∘+90∘=270∘90^{\circ} + 90^{\circ} + 90^{\circ} = 270^{\circ}.\nStep 3: The total sum for a quadrilateral is 360∘360^{\circ}. Subtract the known sum: 360∘−270∘=90∘360^{\circ} - 270^{\circ} = 90^{\circ}.\nStep 4: An angle of 90∘90^{\circ} is called a Right Angle.

Explanation:

We use the rule that a 4-sided shape's angles add up to 360∘360^{\circ} to find the missing corner. Since the result is exactly 90∘90^{\circ}, it is a right angle.