krit.club logo

Shapes and Angles - Degree Clock and Measuring Angles

Grade 5CBSE

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

🔑Concepts

•

An angle is formed when two rays meet at a common point called the vertex. Visually, it looks like a corner or the space between two diverging lines, such as the gap between two open fingers or the corner of a book.

•

The standard unit for measuring angles is degrees, denoted by the symbol ∘^\circ. A full circle or a complete turn is divided into 360360 equal parts, where each part represents 1∘1^\circ.

•

A Degree Clock is a circular tool used to understand angles; it represents a full rotation of 360∘360^\circ. For example, when the hand of the clock moves from 1212 to 33, it covers a quarter of the circle, which is 90∘90^\circ.

•

A Right Angle measures exactly 90∘90^\circ. It looks like the letter 'L' or the corner of a square. In a degree clock, a 14\frac{1}{4} turn always forms 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, like a partially opened pair of scissors 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 looks wide and spread out, like the blades of a ceiling fan or a reclining chair pushed back.

•

A Straight Angle measures exactly 180∘180^\circ. It looks like a perfectly straight flat line. On a degree clock, this represents a 12\frac{1}{2} turn (for example, the hands at 6 o'clock).

•

Measuring angles is typically done using a Protractor, a semi-circular device with markings from 0∘0^\circ to 180∘180^\circ. To measure, you align the center of the protractor with the vertex and the base line with one arm of the angle.

📐Formulae

Right Angle=90∘\text{Right Angle} = 90^\circ

Straight Angle=180∘\text{Straight Angle} = 180^\circ

Full Turn=360∘\text{Full Turn} = 360^\circ

Acute Angle<90∘\text{Acute Angle} < 90^\circ

90∘<Obtuse Angle<180∘90^\circ < \text{Obtuse Angle} < 180^\circ

Angle=Fraction of Turn×360∘\text{Angle} = \text{Fraction of Turn} \times 360^\circ

💡Examples

Problem 1:

What is the measure of the angle formed by the hands of a clock at 3:00, and what type of angle is it?

Solution:

Step 1: A clock is divided into 1212 equal hour divisions. The total angle in a circle is 360∘360^\circ. \ Step 2: Calculate the angle for one hour division: 360∘12=30∘\frac{360^\circ}{12} = 30^\circ. \ Step 3: At 3:00, the minute hand is at 1212 and the hour hand is at 33. This is a gap of 33 hours. \ Step 4: Multiply the hours by the angle per hour: 3×30∘=90∘3 \times 30^\circ = 90^\circ.

Explanation:

Since the angle is exactly 90∘90^\circ, it forms a right angle, resembling the corner of a square.

Problem 2:

If a degree clock shows a 13\frac{1}{3} turn, calculate the angle in degrees and identify the type of angle.

Solution:

Step 1: A full turn in a degree clock is equal to 360∘360^\circ. \ Step 2: To find a 13\frac{1}{3} turn, multiply the fraction by the total degrees: 13×360∘\frac{1}{3} \times 360^\circ. \ Step 3: 360÷3=120∘360 \div 3 = 120^\circ.

Explanation:

The calculated angle is 120∘120^\circ. Since 120∘120^\circ is greater than 90∘90^\circ but less than 180∘180^\circ, it is classified as an obtuse angle.